pakistan building code 1967
TRANSCRIPT
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NO· 141
GOVERNMENT OF WEST PAKISTAN
HIGH\A!AY DEPARTMENT
LAHORE
CODE OF PRACTICE HIGHWAY BRIDGES
1967
SAEED AHMAD, T.Pk., P.S.E.-1
DIRECTOR GENERAL-HIGHWAYS
HOWARD, NEEDLES, TAMMEN & BERGENDOFF, INT. INC. GENERAL HIGHWAY CONSULTANTS
Tl1e purpose or tlLtn <,;Jd~.l ot ?ra.c~:ic,L "1.:; to e.stabl:.sh tnini1nun1 standards and 'l'DLic:i r: p.:cc::;d,Jres End p~e.cti<:efl for the des:Lgr: ot' us!.1al ~ c.f 1tigtr~va:.r struct:.:.:...~~s :_n th.e Province of West Pak1stan. T~·~au~h s~ch st~sdarJization of methods, a Tnuch greater be realized in design
With this in mind this first ~ditlon of th2 r~de hs~ b~en written co cover pr i.mc;.r t reinforced and ~r~strsssed conc=~te design Refer-enc.e has. be.er1 tnade to th"E.~ :s·l_-it·!.sh l-;t~::..r:.dard Spec.ific;:rtions for those special cases vit-1~:re ~:t2;:::1 desLgn ~~~ill be required.
ex pet iei:JCe and the iutu_rs c_~.;s.i.l~.:;-~) Ll.i ty of more econou1ical and different structural mate~ials wiLl dictate the necessity that this Cod2 be revised pericdtcally. It is expected that all those respo.nsibl0 fer ::otructm:e designs 1<vi1l be alert to the need for such revisions. Suggestions for updating the Code along these lim':s are encouraged.
Article
1.1 L2 L3 1.4 1.5 1.6 1.7 L8 L9 l, 10 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.18 1.19 1,20
L21
2.1. 2,2 2,3 2.4 2.5 2.6 2.7 2.8 2 ,.9 2.10 2 011 2.12 2.13 2.14 2.15 2,16 2.,17 2.18
CONTENTS
SECTION 1 - GENERAl, FEATURES OF DESIGN
Preliminary Data Determination of Waterway Area Spacing and Location of Piers and Abutments Vertical Clearances Restricted Waterways Obstruction and River Training Determination of the Haximum Depth of Scour Depth of Foundations Size of Culverts Openings Length of Culverts Width of Roadway and SidewalL Clearances Curbs & Safety Curbs. Railings Roadway Drainage Supereleva.tion Floor Surfaces Utilities Roadway Width, Curbs and Clearance for Tunnels. Roadway Width, Curbs and Clearance for Underpasses (undivided Highways) Roadway Width, Curbs and Clearances for depressed Roadway
SECTION 2 - LOADS
T ... oads Dead Load Live Load Highway Loadings Standard Truck-Train Loading Application of Loadings Reduction in Load Intensity Sidewalk, Curb, Safety Curb and Railing Loading Impact Longitudinal Forces Wind Loads Thermal Forces Uplift Force of Stream Current Buoyancy Earth Pressure Earthquake Stresses Centrifugal Forces
i
1-l 1-5 1-8 1-8 1-9 1-9 1-9 1-11 1-13 1-13 1-13 1-13 1-14 1-14 l-15 1-15 l-15 1-15 1-16
1-17
1-18
2-1 2-1 2-3 2-3 2-3 2-5 2-5 2-6 2-7 2-8 2-9 2-11 2-12 2-12 2-13 2-13 2-14 2-14
Article
SEC'!'ION 3 - DISTRIBU'I'IO:~ U? LOAI;S
3o 1, Distribution of Wheel Loads to Stringers, Lcr:git:.~dL1ai
4.1 4.2 4.3 4.4 4,,5
5.1 5.2 5 .. 3 5.4
6 .. 3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 6.11
7.1 7.2 7.3 7 o4 7oS 7.6 7.7 7 .. 8 7.9
Beams and Floor Beams Distribatic.n of Loads and Design ot Cor:crete Slabs Distribution of Wheel Loads through Earth Fills
SECTION 4 - HILITARY l.0ADING
Loading Horizontal Clearance Distribr;tion of Load to 1.-o::gitudinal Stringsrs Impact Distribat io:.~ cf Loads and Dt:'.s ig-;:1 of Concret<.:>. Slabs
SECTIO"N 5 - illiiT STRESSES
General Concrete Stresses ReinforcP.ment Steel Stressr.:s
SECTION 6 - CONCRETE DESIGN
Ge;:1eral Assumptions Span Lengths Expansion T-Bea.ms Reinforcement Compression Reinforcement L:'t B<::ams Web Reinforcement Columns Concrete Arches Viaduct Bents and Towers Box Girders
SECTION 7 - PRESTRESSED CONCRETE
General Notation Design Theory Basic Assumptions Loading Stages Load Factors Allowable Stresses Loss of Prestress Flexure
ii
3-1 3-2 3-6
!.; -1
4-2 4-2
5-l 5-2 5-3 5-3
6-1 6-2 c. " u-L
6-3 6··4 6-6 6-6 6-9 6-16 6-17 6-18
7-1 7-1 7-3 7-3 7-3 7-4 7-4 7-5 7-7
Article
7.10 7.11 7.12 7.13 7.14 7.15 7.16 7.17 7.18 7.19
8.1 8.2 8.3
9.1 9.2 9.3 9.4 9.5
10.1
Ultimate Flexural Strength Maximum and Minimum Steel Percentage
· Nonprestressed Reinforcement Shear Composite Structures End Zone of Concrete I-Beams Cover and Spacing of Prestressing Steel Embedment of Prestressing Strand Concrete Strength at Stress Transfer Reinforcement in Beams
SECTION 8 - PILE LOADS AND BEARING POWER OF SOILS
Bearing Power of Foundation Soils Angles of Repose Bearing Value of Piling
SECTION 9 - SUBSTRUCTL~ES & RETAINING WALLS
Piles Footings Abutments Retaining Walls Piers
SECTION 10 - STEEL DESIGN
Design and Construction
iii
7-7 7-9 7-9 7-10 7-11 7-12 7-12 7-13 7-13 7-13
8-1 8-1 8-2
9-1 9-4 9-7 9-8 9-9
10-1
SECTION l - GENERAL FEA1~RES OF DESIGN
l < l PRELl NI ;\lARY DATA
The following information <,.;ill normallJ' be required for the proper design of structur2s.
A. STREAM CROSStNG~
(]) An 1ndex map to a suitable smdll scale ltopo she~ts scale one i Pch to one mile would do ir. most cases) showing the proposed locat ton of the bridge, the alternative :.;i.tes investigated and rejected, the ex·i_st ing comm•1nicat ions, the general topography of the country, and the important towns, etc., in the 'Jicinity.
{2) [\ contour survey plan of the stream showing all topographical fentures extending to the distance shown below(or such other greater distances as the engineer restonsible for the design may direct) upstream and dmvnstream of any of the preposed sites ar,d to a sufficient distance on either side to give a clear indication of topographical or OT:her features that might influence the location and design of the bridge and its a~proaches. All sites for crossings worth consideration shall be shown on the plan.
(a) 300 feet for catchment area less than one square mile (scale not less than one inch to 100 feet).
(b) 1000 feet for catchment areas of 5 square miles (scale not less than one inch to 100 feet).
(c) One mile for catchment areas of more than 5 square miles (Scale not less than one inch to 330 feet).
Note:- In djfficult country and for crossings over artificial channels the engineer responsible for the design may permit discretion to be used regarding the3e limits of distance,provided that the plans give sufficient information on the course of the stream and the topographical features near the bridge site.
(3) A site plan to a suitable scale showing details of the site selected and extending not les(:> than 300 feet upstream and downstream from the centre line of the crossing and covering the approaches to a sufficient distance which in the case of a large bridge shall be not less than a quarter of a mile on either side of the stream. The plan shall include all information that is essential for complete and proper appreciation of the project. The normal requirements are given below;
(a) The name of the stream or bridge and of the road and the identification number allotted to the crossing;
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(b) The approximate outlines of the banks, the high water channel(if different from the banks), and the lmv water channels with contours at suitable level intervals in the bed anJ beyond the banks and the line of the deepest points along the dry weather channel;
(c) The direction of flow of 1vater at maximum discharge end if possible, the extent of deviation at lc~er discharge;
(d) The alignment of existing approaches and of the proposed crossing and its approache,s;
(e) The angle and direction of sk2w if the crossing is aligned on a skew;
(f) The name of the nearest inha:).Lu"d identifiable locality at either end of the crossing on the roads leading to the site;
(g) References to the position(\vir:h description ar.d reduced level) of the bench mark used as datum;
(h) The lines and identificatiou numbers of the crosssec::ions and logitudinal section taken Hith!_n the scope of the site plan, and the exact location of their extreme points,
(i) The locations of trial pits or borings each being gh'en an identification number;
(j) The location of all nullahs, buildings, wells, outcrops of rocks, and other possible obstructions to a road alignment.
(4) A cross-section of the stream at the site of the proposed crossing ( Scale not less than one inch to 100 feet horizontally , exaggerated vertically to a scale of not less than one inch to 10 feet) and indicating the following information:
(a) The name of the stream and the serial number allotted to the crossing;
(b) The name of the road with mileage and chainage of the centre of the crossing;
(c) The bed line up to the top of the banks and the ground line to a sufficient distance beyond the edges of the stream, with levels at intervals sufficiently close to give a clear outline of markedly uneven features of the bed or ground showing right and left bank and names of villages on each side;
1-2
(d) The nature of the surface soil in bed, banks and approa, ches, with trial pit or bore hole sect ion.s showing the levels and nature of the various strata down to hard strata suitable for foundation and the safe intensity ot pressure on the foundation soil; (as far as practicable, the spacing of trial pits or bore holes should be such as to provide a full description of all substrata layers along the \vl:ole lengt.b and >,vidth of the crossing);
(e) The low water level;
(f) The ordinary Flood level;
(g) The highest flood h:vel and the yo::,ars in which it occur, red. State iE the flood level is affected by back-water and if so, give details;
(h) The catchment area, maximum discharge specified in Article 1.:2(A.) arvl correspo~1ding average velocitiJ a:: tbe site of the crossi~g;
(i.) The estimated depth of sco:.;r oc, if the scour depth has been observed, the depth of scour, with details of obstructions or of any other special causes responsible for the scour.
(5) -\ lo·;-·J_gitudinal ~:;ection of the strecr~n snov11Eg tbt .site oj the bridge with the highest flood lev2l, the ordiGary flood level, the low water level, and the bed levels at suitably spaced intervals along the approximate centre line of the deep water cha~nel between the extreme p~.dnts ~-:; \vhich the survey map required in Article 1.1A(2) e:ztends, The horizontal scah' not let=:s than one inch to 100 f.efi!t.
{6) A note givi:~.g as iar as possible ti;e following particulars relating to the catchment area;
(a) Jbe size of the catchment;
(:;) The shape or the catchment;
(c) The intensity and frequency of rai.nfall in the catchment;
(d} The slope of the catchment, both longitudinal and transverse;
(e) The nature of the catchment, whether under forests, under cultivation, urban etc;
(f) The nature of the soil crust, porous or rocky, etc;
(g) The possibility of subsequent changes in the catchment like afforestation, deforestation, urban development, extent of reduction in cultivated area, etc;
(h) Storage in the catchment artificial or natural.
(7) A chart of the periods of high flood levels for as many years as the relevant data are recorded.
(8) A note giving important details of the bridges, if any, crossing the same river within a reasonable dist:auce oE the proposed bridge.
(9) The minimum permissible vertical ch~Hl!le:l clearar:ce and the b<1sis on which it has been determined mentioning any special requireme<lts for navigation.
(10) Liability of the site of earthquake disturbances.
(11) A brief description of the reasons for selection of the particular site for the crossing accompanied, if necessary , '"ith typical crosf"= section of the stream at suitable alternative crossing places both upstream and downstream of the selected site.
(12) Sub-soil data of the stream at the site of the bridge should te obtained at four or more points in the cross section.
(13) All other pertinent information affecting the design such as:
(a) Width of roadway curb to curb (b) Vertical and horizontal a~ignment (c) Cross Slopes (d) Live Load to be applied (e) Safety Curb, footpatb and/or animal path (f) Utilities to be carried by the superstructure (g) Location and type of piers and foundations (h) Freeboard Clearance
(14) In case of streams having discharge over 50,000 cusecs, the hydraulic design should be checked by model studies. The following data shall be required.
(a) A site plan showing the location of the bridge with respect to the stream. A stretch at least 5 miles up stream and 3 miles down stream or two 'S' curves up stream and one 'S' curve down stream of bridge, whichever is longer, should be given on the plan. In order to indicate its dominent course, the course"·Of the river or stream over a five (5) years period should be shown.
(b) The cross sections of the stream should be observed
1-4
at intervals 1000 ft. apart in straight reaches and 500 ft. apart along curves for proper representation on the model. The location of all cross sections should be marked on the site plan.
(c) Gauge discharge curves and hydrograph of the stream at the bridge site should be collected for the last 5 to 10 years. If such data is not ave.ilable, data pertaining to the hydrographs and guage discharge of the rr;_ain stream, up stream and down stream of the site may be used.
B. H1GHI-IA'f AND RAILROAD CROSSINGS
(1) An index map to a suitable small scale (topo sheets scale one iw_h to one mile wou.ld do in most cases) shmving the proposed location of tht.: bridge, t:he exist5_ng communications, the important towns etc., in the vicinity.
(2) A plan and elevation of the proposed bridge showing span lengths; critical vertical clearance of superstructure required above roadway or railroad; critical horizontal clearance to piers and abutments; depth of structure hom profile grade to bottom of grider; location and number of bore holeL;;; and the profile of the bridge and its approaches.
(3) A cross section of the proposed bridge showing the number, £ype and spacing of girders; the thickness of slab; the cross slope; width ,-,f roadway curb to curb; the width of <>afety walk, footpath and/or animal path, and the utilities to be carried by the superstructure.
(4) A profile of the highway or railroad.
(5) A cross section of the highway or railroad.
(6) Type of pier to be used.
(7) Type of footing to be used, whether rock bearing, soil bearing or pile bearing and the allowable capacities of each.
(8) Live load to be applied.
1. 2- DETERMINATION OF WATERWAY AREA
For the determination of the \vaten1ay area UJ. be provided for a stream crossing or culvert, a careful study shall be made of local conditions, including flood height, flov;r and frequency, size and performance of other openings in the vicinitY carrying the same stream, characteristics of the channel and of the watershed area, available rainfall records and any other information pertinent to the problem and likely to affect the safety 'or economy of the structure.
l-5
'(A) The maximum discharge >-Ihich the stream crossing or culvert shall be designed to pass shall be determined by a consideration of the following methods:
(1) From the rainfall and other characteristics of the catchment which together from the general formula;
n Q = c X A
Where Q is the maximum flood discharge in cubic feet per second (cusecs), A is the area of catchment of the stream in square miles, 11 n 11
an exponent varying from 0.5 to 1.0, and C a varying coefficient depending upon the characteristics of the terrain. Some typical formulas are:
(a) Dicken's formula
Q = c X A 3/4
Where C is equal to 750 for mountainous areas and 500 for planes
(b) Ryves formula
Q = c X A 213
Where C is equal to 500 for mountainous area and 350 for planes.
(C) Inglis formula
Q 7000 A
VA+ 4
(d) M.E.S. formula
1/2 Q = 2100 X A
(2) From the hydraulic characteristics of the stream such as the cross-sectional area, and slope of the stream allowing for velocity of flm.;r. In this method the velocity is obtained from the formula
1.486 2/3 1/2 V = X r X S
n
Where r = hydraulic mean depth in feet S Slope V mean velocity in feet per second n coefficient of rugosity of stream bed
1-6
n 0.020 for ea.rth in good order and regimen~ free from stones and weeds
0.025 for· earth in fair order and regimen, free from stones and weeds
0.030 for earth in bad order, with occasional stones and weeds
0.035 for streams in bad order and. regimen with stones and weeds
0.050 for torrential rivers in beds covered with detritus and boulders.
The velocity thus obtained is then multiplied by the crosssectional area to give the required discharge Q.
(3) From the Unit Hydrograph method
The results from the above methods should then be compared and with proper judgement, arrive .. at the design discharge to be used.
(B) Having arrived at an estimate of required discharge either by the calculations from the preceding sections or by flood data secured fro1n ~vailable reports of gauging stations or local high water marks, the next step is to design an opening that ·will pass this amount of water without damage to the Btructure or to adjacent work or properties.
(1) For artificial irrigation, navigation, and drainage channels, the effect~ve width of waterway shall generally be equal to the width of channel at mid~depth, but concurrence shall be obtained invariably from the authority controlling the channel.
If it is proposed to flume the channel at the site of the bridge, the flurning shall be subject to the consent of the same authority and in accordance with its essential requirements.
(2.) For nonmeandering natural streams not widE. than 100 feet in alluvial beds but with well-defined banks and for all natural channels in beds with rigid inerodible boundries, the width of waten1ay shall be the distance between banks at that water ;.;ul·face elevation at which the designed discharg~ was determined.
(3) For large natural streams in alluvial beds and having undefined banks, the width of waterway shall be determined from the design discharge, using some accepted rational formula such as Lacey's formula for a regime flow condition where
1/2 p = 2.67 Q P being the wetted perimeter in feet,
and Q the discharge in cusecs of a stream consisting of alluvial beds like sand, or clay, transported and deposited by flowing water.
1-7
The \vetted perimeter thus obtained for a straight reach of the stream is very nearly the effective width of waterway in such cases.
SPACING AND LOCATION OF PIERS AND ABUTMENTS
The following consideration shall govern the spacing and location of .nd abutments:
(a) Piers and abutments shall be so located as to make the best use of the foundation conditions available.
(b) Subject to (a) above, the suitable economical span shall be adopted, modified, if necessary, to suit navigational and aesthetic requirements. The number of piers should be limited as much as is practicable, they catch debris and thus the effective waterway could be reduced substantially.
(c) The alignment of piers and abutments shall, as far as possible, be parallel to the mean direction of flmv in the stream but provision shall be made against harmful effects on the stability of the bridge structure and on the maintenance of adjacent stream banks caused by any temporary variations in the direction and velocity of the stream current.
VERTICAL CLEARANCES
Clearance shall be allowed according to navigational or anti-:tion requirements or, where these condition do not arise, ordinarily .OWS:
(a) For o1~enings of high level bridges, which are approximately rectangular, or with a very flat curve of the soffit of super-structure, as for instance in the case of beam, frame, or bowstring superstructures, continuous girders or open spandral arches •vith suspended decking, the minimum clearance shall be in accordance with the following table:
DISCHARGE
Below 10 cusecs 10-100 cusecs 101-1000 cusecs 1001-10,000 cusecs 10,001-100,000 cusecs Over 100,000 cusecs
MINIMUM VERTICAL CLEARANCE
Ft. In. 0 6 1 6 2 0 3 0 4 0 5 0
The minimum clearance shall be measured from the lowest point
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1 ,. "1_,.-.
~. J
of the deck structure inclusive of main girders in the central half of the clear opening.
(b) In structures provided '>vith metallic bearings such vertical clearance shall be allowed as will ~revent the submergence of those bearings.
(c) In the case of artificial channels, e.g., irrigation canals having controlled flov-1 and carrying no floating debris, the Engineer~in·Charge may at his discretion provide less vertical clearance than that specified in sub-clauses (a) and (b) above.
RESTRICTED WATERWAYS
When it is necessary to restrict the waterway to such an extent that the resultant afflux will cause the stream to discharge at erosive velocities, protection agains~ damage by scour shall be afforded by deep foundations, C'J.rtain or cut·"off walls~ rip-rap, bearing piles, or other euitable means" Likewise embankment slopes adjacent to a 11 structures subject to erosion nhall be adequately protected by pitching, revetment walls or other suitable const-ruction.
1. 6- OBSTRUCTION AND RIVER TRAINING
Obstructions in the river bed likely to divert the current or c3use undue disturbed flow or scour and thereby endanger the safety of the bridge shall be r:::mov('.'d as far as practicable for some distance upstream and down~ stream of the bridge depending on the river characteristics. Attention shall be given to river training and pro tee tion of banks over such lengths of the river as require it.
L /c DETERMINATION OF THE MAXIMUM DEPTH OF SCOUR
(A) The maximum depth of scour in a stream shall be ascertained whenever possible, by actual soundings at or near the site proposed for Lhe bridge, during a flood before the. scour holes have had time to silt up appreciably. Due allowance shall be made in the observed depth for increase in scour resulting from
(1) The design discharge being greater than the flood discharge during which the scour was observed;
(2) The increase in velocity due to the obstruction in flow caused by construction of the bridge.
(B) Where the practical method of determining scour described at(A) above is not possible, the following emperical approach may be used as guide
when dealing with natural streams in alluvial beds:
For regime conditions in a stable channel 1/3
d = 0.473(+)
For restricted flow
l1aterial
( q2 )1/3 d = k 0.9
f
d Normal depth of scour below H.F.L.(high flood level)
Q Total design discharge in cusecs
q Design discharge per foot of width in cusecs
k A factor varying from 1 to 3 derending on local conditions. For a major stream crossing the factor to be used shall be decided on consultation with the Directors of the Bridge and Research Directorates.
f Lacy's silt factor for a representative sample of the bed material. The silt factor is' approximately equal to 1. 76 m% where m is the wetted mean diameter in milimeters (rnm) of the bed material. See table for value of f given by Lacy for various grades of bed material
LACY'S SILT FACTOR
f
Medium silt, canges canal distributary Standard silt, Punjab data
00.233 00.323 00.505 00.725 00.988 01.290 02.420 07.280 26.100 50.100
00.850 01. 000 01.250 01.500 01. 7 50 02.000 02.750 04.750 09.000 12.000
Medium sand Coarse sand Fine Bajri and sand Heavy sand Coarse Bajri and sand Coarse gravel Gravel and bajri Boulders and Gravel
The maximum depth of scour shall be taken as follows:
(1) In a straight reach 1. 5 d
(2) at a right angle bend 2. 0 d
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(3)
(4)
at noses of piers
at upstream noses of guide banks
2.0 d
2.5 d
Due allowance shall be made for a::.1 increase in concentration of flovJ through a portion of the waterway.
\-There the computed depth of scour ceachss 'AI'"ll into layers, as iadicated by boring informatior;, oi: relatively scour free material (i, e, gravel and boulders) the computed depth of scour may be red1.<ced.
1 .. 8~ DEPTH Of FOUNDl\l'IONS
(A) The depth of foundations shall be d\~termi:J.ed by consideration of ~he safe hearing capacity of th~ soil after taking into account the effect of sco-ur.,
(B) In all doubtful cases, the bearing capacity of the foundation ,oni} shall be determined by actual loading tests. The adequate th.ickne133 cf the foundation bearing layer of the soil shall be ascertained by borings o:r trial pits ..
) l'he maxirnum toe pressure o:n the foundatir:;r. bearing l"l.y~r
t"e.sulting fro!n t1:-te ~vorst: cornb:l~~1ati.on. of dir£,_ct forc2s a::td ov·ert:jrilirtg mo1nex.1~.s
:~hn11 h<.; cB.lcuJat!"d f:or each individt:al fouadaticn. In calcul'l'::ing this prcssure 1 the. (~ffect of passi,/e. rr-.::~i.stance of the earth of t.~he. sides of th~)
foundation structure. ,nay be taken h:to Hcco:.mt be low the ma;...:1mum depth of the scour only The effect of skin friction on the sides of the foundation :;tructure may be ignored normally except in the ca~;e of well and pile. ntructures where skin friction may be allowed on the pcrtion below the maxi:mum d~'pth of scour.
(D) lllhere a substantial stratum of solid rock, or other material inerodible at the anticipated maximum velocity and of adequate safe bearing capacity, is encoJntered at a shallow depth below the surface, the foundatic•n shall be taken into that stratum and securely bonded or if necessary anchored to it.
(E) Where only erodible strata are available, the fo:.mdations may be designed either as "Deep" or as ~:Shallow" but in such a manner that ii:l either case the safe bearing capacity of the sub~soil is not exceededo
(1) DEEP FOUNDATIONS (in erodible strata) If 'd' is the anticipated maximum depth of scour below the designed highest flood level includ" ing that on account of possible concentration of flow, the minimum depth of foundation below H.F.L, shall be 1.33 d. The Depth below the scour line shall in no case be less than six feet for piers and
1-11
Note:
HORIZONT.D..L CLEl\f.<ANCE r------ ·---------- 1 ~·--------------~-----,--~--------~=------1
' MINIMUM ROADWAY WIDTH
:T LEAST 4FT. GREATER THAN
APPROACH PAVEMENT WIDTH ..,1 BUT NOT LESS THAN 24 FT.
CLEARANCE DIAGRAM TWO LANE HIGHWAY TRAFFIC
FIGURE I
For heavy traffic roads, roadway widths greater than the above minima are recommended.
For all bridges under 50 feet in length, the over-all width should conform as nearly as practicable to the full shoulder-to-shoulder width of the highway.
For recommendations as to roadway widths for the various volumes of traffic see the Highway Design Manualo
1-12
abutments supporting other types of superstructure. The foundations shall in all cases be taken down to a depth \vhich will provide proper grip according to some rational method.
(2) SHALLmv FOUNDATIONS (in erodible strata). Foundations may be taken dmm to a comparatively shallow depth belo\v the bed surface provided the foundation bearing stratum is practically incompressible (e.g.sand), is prevented from lateral movement, and is also protected against scour.
1.9- SIZE OF CULVERT OPENINGS
In general, culverts shall be proportioned to carry the maximum flood discharge without head. If the maximum flood discharge occurs only at rare intervals,culverts may be designed to carry it under slight head, provided they are protected against undermining by means of adequate pavement and apron or cut-off walls and that adjacent embankments are protected from erosion by rip-rap or other suitable means.
1.10- LENGTH OF CULVERTS
The length of culverts shall be sufficient to provide the required 1ATi.dth of roadway embankment. 111e assumed slope of the embankment shall be suitable for the particular filling material and shall be such as to eliminate any tendency for the embankment slopes to slip or slide.
1.11~ WIDTH OF ROAmvAY AND SIDEWALK
The \vidth of roadway shall be the clear width measured at right angles to the longitudinal centre line of the bridge between the bottoms of curbs or guard timbers, or, in the case of multiple height curbs, between the bottoms of the lower risers. The width of the sidewalk shall be the clear width, measured at right angles to the longitudinal centre line of the bridge, from the extreme inside portion of the handrail to top of the face of the curb or guard timber, except that if there is a truss, girder, or parapet wall adjacent to the roadway curb, the width shall be measured to its extreme walk side portion.
1.12· CLEARANCES
The horizontal clearance shall be the clear width, and the vertical clearance the clear height, available for the passage of vehicular traffic as shown on the clearance diagrams.
Unless otherwise provided, the several parts of the structure shall be constructed to secure the following limiting dimensions or clearances for traffic.
The clearances and width of roadway for 2-lane traffic shall be not less than those shown in Figure 1. The roadway width shall be increased at least 10 feet and preferably 12 feet for each additional lane of traffic.
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1.13~ CURBS AND SAFETY CURBS
The face of the roadway curb is defined as the battered or sloping surface on the roadway side of the curb. Preferably vertical c•.a-bs shall not: be used, Horizontal measurements of roadvn'l and curb >•Jidth q;::c_. given fTom cl:ce bottom of the face, or, in the case of stPp8ei back curb, fro~ the ~ottom of the lmver face for roadway width,
The fuce of Lhe roadway curh pre fc-c-aLl;· sha 11 he not 1e::: s t!-.:n1 12 inche::; and in no instance less than 9 i.~•r:i--,".:·· !rc.m ::ha: p,wt :c:''' ,,f •:h·=: structu;,' above the elevation of the top of the CL.lTb awl n2are.st the road',vay. 1.r1 ca.;:;es
of bridges in which the clear roadvJay widtr1 :i:; eqt:al !.o or great,,,, ,_:,,~;:-, th~;
sho,~lder width but: not less than the approa~·rt pavenl9Et width plu:c; 12 fe.;>::, curbs may be omitted. In urban areas~ the cur~1 ht•igl1t shall no:. b"! less ~1-:;;..-:::
7 inches above the adjacent finished surfac(' of the :roadway, anr:l L1 -c;\ra.l areas not less than 9 inches above the adjacent f ird. '-'h,:·.d "Jurfac2 of ttH~ rva(hvay. That portion of a curb more than 10 inches above the roadwa·y sur:-a.c~o: sba.ll b2 stepped back or sloped back so that no part of the vehicle except the tires may come in contact with it. Curbs widened to provide for occasional pedestrian traffic shall be designated "Saiety cnr::,3n. Safety curbs shall be not less than l 1 -6" wide.
RAILINGS
Railing shall be provided at the edge of scntctures for the prou-ci.:Lon of traffic, or for the protection of pedestria-::,s, or both. W11ere pe.d'::stri_':l!1 footpaths are provided adjacent the roadways, n :r3.ffic railing ma.y he provided between the two with a ~edestrian railing outsid2, or a combination trafficpedestrian railing may be provided outside.
Curbs shall be provided between roadways and pedP~trian footpaths unlesa a traffic barrier separates the two.
A, TRAFFIC RAILING
While the primary purpose of traffic railing i;> to contain the average vehicle using the structure, consideration should al2o be given to protection of the occupants of a vehicle in collision with the railing, to protecl:ioo of other vehicles near the collision, and to appearance a~d freedom of view of passing VBhicles.
Material for traffic railing shall i::-e concre t.e, clletB.l, 1.mber c1· r-t
combination. Metal materials with less than 10 per cent tested elongat:icn• shall not be used. Preference should be given to pro'Jiding a smootb, continuous face of rail on the traffic side with che posts set back £rom the face of the rail. Structural continuity in the rail members, including anchorage of free ends is essential. Where joints are required in the lengths of railings, the construction shall be reinforced by reduced post spacing, by splice material in the rails, by bolting or welding.
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The height of traffic railing shall be not less than 2'-3" measured from the top of the roadway, or curb, to the top of the upper rail member.
Careful attention should be given to the treatment of railing at the bridge ends. Exposed rail ends and sharp changes in the geometry of the roadway shall be avoided.
B. PEDESTRIAN RAILING
Railing components shall be proportioned commensurate with the type and volume of anticipated pedestrians, takir.g account of appearance, safety and freedom of view of passing vehicles.
Materials for pedestrian railing may be concrete, metal, timber, or a combination" 1be minimum height of pedestrian railing shall be 3'-0" (a preferred height is 3'-6") measured from the top of the footpath to the top of the upper rail member,
J., 15·- ROADWAY DRAINAGE
The transverse drainage of road~vays shall be secured by means of a tmitable crown in the roadway surface and longitudinal drainage by camber or gradient. If necessary, longitudinal drainage shall be se~ured by means of scuppers, inlets or other suitable means, which shall be of sufficient ;.;J.ze and numbe:r to drain the gutters adequately. If drainage fixtures and downspouts are required, the downspouts shall be of rigid corrosion-resistant material not less than 4 inches in least dimension, provided with suitable clean~ out fixtures. The details of floor drains shall be such as to prevent the discharge of drainage water against any portior. of the structure. Over-hanging portions of con£rete floors preferably shall be provided with drip beads,
L 16- SUPERELEVATION
The superelevation of the floor surface of a bridge on a horizontal curve shall be provided in accordance with the geometric design criteria for highways, except that the superelevation shall not exceed .08 foot per foot width of roadway.
L 17- FLOOR SURFACES
All bridge floors shall have skid-resistant characteristics.
1. 18- UTILITIES
Where required, provlslon shall be made for electric conduits, telephone conduits, water pipes and gas pipes.
1-15
1. 1 :J- ROADWAY WIDTH, CURBS A~1D CLEARANCES FOR TUNNELS (See Figure 2.)
(A) Roadway \\Tidth - The clear width bet,Jeen curbs shall be Lot lc~:-:o
than that specified for bridges.
(B) Clearance bet'-Jeen Halls - The minimum ':vid th bet\1een VJd lls of two-lane tunnels shall be 30 feet.
(C) Curbs - The '#idth of curbs shall be not less than .U:J
height of curbs shall be as specified for bridges. ch.t~s. The
(D) Vertical Clearanc:e - TI1e vertica1 clearance, bet\AJeen (::~1rbs sht1L1 be not less than 16'-6 11 •
CLEARANCE DIAGRAM FOR TUNNEL TWO LANE HIGHWAY TRAFFIC
FIGURE 2
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CLEARANCE T~NO LA
F\()t\D\\!.1.\Y v~rlO-TH
t~\)"j" LESS YTi'-~i~.Pi
.t'U11l FOR UNDER HIGHW.LW TRAFFiC
FIGURE 3
1. 20- ROAmvAY WIDTH, CURBS AND CLEA.H;\.NCES :FOR UNDERPASSES
(UNDIVIDED HIGH\-fAYS) (See Figure 3.)
(A) \-Jidths - The clear lividth bet\\Ieen -.;v-alls or columns shall be not less than 6 feet wider than the approach pavement, but in no case shall the width be less than 30 feet.
(B) Vertical Clearance - A vertical clearance of not less than 16 '-6 11 shall be provided between curbs, or if curbs ar.e not used, over the entire width that is available for traffic.
(C) Curbs - Curbs shall not be less than 18 inches in width, The height of curbs shall be as specified for bridges.
1-17
l. 21~ ROAmJAY WIDTH~ CURBS AND CLEARANCE FOR DEPRESSED ROADWAYS
(A) Roadway Width-~ The clear \vidth between curbs shall preferably be not less than that speciEied for bridges.
(B) Clearance Between Walls - The minimum width between walls for depressed roadways carrying t>vo lanes of traffic shall be 30 feet.
(C) Curbs= The width of curbs shall be not less than 18 inches. The height of curbs shall be as specified for bridges.
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SECTION 2 - LOADS
2.1 - LOADS
Structures shall be proportioned for the following loads and forces when they exist:
and 7.
1. Dead load 2. Live load 3. Impact or dynamic effect of the live load 4. Wind loads 5. Horizontal forces due to water currents 6. Longitudinal forces caused by the tractive effort of
vehicles or by braking of vehicles and/or those caused by restraint to movements of free bearings.
7. Centrifugal forces 8. Buoyancy 9. Earth pressure
10. Thermal forces 11. Shrinkage stresses 12. Rib shortening 13. Secondary stresses 14. Erection stresses 15. Earthquake stresses.
Hembers shall be proportioned as specified under stresses, Section 5
Upon the stress sheets a diagram or notation of the assumed live loads shall be shown separately.
t-Jhere required by design conditions, concrete placing sequence shall be indicated on the plans.
2.2 - DEAD LOAD
The dead load carried by a member shall consist of the portion of the weight of superstructure (and the fixed loads carried thereon), which is supported wholly or in part by the girder or member including its own weight. The following unit weight of materials shall be used in determining loads:
Naterial
1. Ashlar or Coarse Rubble Masonry
2. Brickwork 3. Cast Iron 4. Asphalt Concrete 5. Cement Concrete, plain
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Lbs./Cu. Ft.
150 120 450 140 140
Materials Lbs./Cu.Ft.
6. Cement Concrete,reinforced 150 110 140 490
7. Earth (Compacted) 8. Macadam (binder premix) 9, Rolled Steel
10. Sand (loose) 11. Sand (wet compressed)
90 120 100 62.5 so
480
12. Stone Metal 13. Hater 14. Wood 15. Wrought iron
A. LOAD ON CULVERTS
Earth pressure or load on culverts will be computed as the >veight of earth directly above the slab.
B. RIGID CULVERTS
For definite conditions of bedding and backfill, the principles of soil mechanics rnay be applied. The following are recommended formulas for these conditions:
(1) Culvert in trench or unyielding subgrade, or culvert untrenched on yielding foundation.
P = WH
(2) Culvert untrenched on unyielding foundation (such as rock or piles)
P W (1.92 H- 0.87B) for H > 1.7 B;
k P 2, 59 BW ( e - 1) for H <:: 1. 7 B
Where K = 0 · 385 H
Where P
E
H
w E
B
the unit pressure in pounds per square foot due to earth backfill
width in feet of trench, or in case there is no trench, the over=all width of the culvert
depth in feet of fill over culvert
effective weight per cubic foot of fill material
2.7182818 =base of natural logarithms,abstract number
2=2
C. SHEAR IN SLABS
The maximum shear in the top and bottom slabs shall be assumed to occur at a distance out from the face of the wall or abutment eqL:al to the thickness of the slab, Hhen haunches are provided at the corners of the cells, their effect shall be excluded from the design.
D. NEGATIVE MG1>1ENTS IN SLAB AND t;JALLS
The maximum negative moments shall be taken at the face o£ the wall for the top and bottom slabs and at the underside of th6 top slab and top of the bottom slab for the walls or abutment, Bond shall be computed at the same section as for moments.
2.3- LIVE LOAD
The live load shall consist of the weight of the applied moving load of vehicles, cars and pedestrians.
2,4- HIGHWAY LOADINGS
General
The highway live loading on the ro2v:hvays of bridges or incidental structures shall consist of a standa.rd truck ·· train. Two systems of loading are provided for Class nA" loading artd Class "B" loading,
B. Class "A" Loading,.
The class "N' loading ts illustrated in figure 4, It consists of a four-axle truck with two two-axle trailors ..
C, Class "B 11 Loading
The Class 11B11 loading shall be identica 1 to Class ''N' loading except. for the axle loads which shall be 60';~ of Class A Loading.
2.5- STANDARD TRUCK - TP~IN LOADING
The wheel spacing, weight distribution, and clearance of the standard loading shall be as shmv'l1 in Figures 4 with the following conditions;
(1) \Hthin curb to curb width of the roadway, the standard vehicle or train shall be assumed to travel parallel to the length of the bridge, and to occupy any position, which will produce maxhnum stresses, provided that the minimum clearanc-:es bstween a. vehicle and the roadway face of a curb and bet~veen two passing or crossing vehicles, as shown in figure 4, are not encroached upon,.
(2) For each standard vehicle or train, all the axles of a unit
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N •
.f"-
~~
~---] -----l :;------1 --·---------:! --~ ·----------)";";1
s (, ' i
s~~ .~ .. r -1-~ ""''"'1,_~-. . ........ ,.~-~"~~~"··· -- ...J-..L.w.
L!UITJNG POSITION OF STANOMD ''fRUCK ~TRAil\! LOArHI•§G
WITH REFERENCE TO A TRAFFIC LANE (For ground con! oct areo and value of ·~ •: se& tobh! i r.m<l 2 )
FIGURE 4 LOADING CLASS '~" FOR HIGHWAY BRIDGES
~ ;:,_
~ ll
10'-0" 10'-0" __ 65~~ -r1
15,000 Lbs.
15,000 Lbs.
15POO 6,000 6,000 Lbs. Lbs. Lbs.
·---- I ----- GRrJl:JND CONTACTi
CLASS OF LOADING I'"E WAD - _111"''-1 (L.hs) 8 W
----------r'2:5,ooo 10- zo "A'' I 15,000 8 . 15
. ·-~---~6,00~-- ~- 8
I . "B" ' ';:g~ : I ,'i L ___________ j__ 3, soo _s _ __j______!__
TABLE I
'li0TE. Closs "e" loading will hove similar speGificotions to class "A" loading
with the only differef\ce !hoi the oxie loads of class "a" :shall be
oOfo of cia s s ':0.'~
--,------------CLEAR ROAD WIDTH I'IJfl
16'- a" or less 0 ------~
16.- 8 .. to fa'-O"·pm;·.:;.:,eiog uniformly from o to 1':.. 4"
18'-0"to~ ditto 1'-tJ!'to 4'-o'' ~4'~ _ _j__ _____ ._ 4'- o" ~
TABLE 2
of vehicles shall be considered as acting simultaneously in a position causing maximum stresses.
(3) Vehicles in adjacent lanes shall be taken as headed in the direction producing maximum stresses.
(4) The spaces on the carriage vJay left uncovered by the standard train or vehicles shall be assumed as not subject to any additional live load.
APPLICATION OF LOADINGS
Truck-Train Units
In computing stresses, each single standard truck-train shall be considered as a unit, and fractional widths or fractional trucks shall not be used,
B. Numoer and Position, Truck-Train Loadings
Th~ number of the truck train loadings and position as specified in Art. 2.5 shall be such as to produce maximum stress, subject to the reduction specified in Article 2.7.
C. Continuous Spans
On continuous spans one or both trailers sl-,:Jll be removed if \vorst conditions are produced by doing so.
2 7-.' REDUCTION IN LOAD INTENSITY
Where maximum stresses are produced in any member by more than one 3imultaneous truck=train load, the following percentages of the result;,;-~t ltve load stresses shall be used in view of improbable coincident maximum loading:
Per cent
One or two,truck train Loadings 100 ·--~-~-- '. : ·: - -:· _; ----·- " ., .. - ~ - - -"l
Three ·nuck train load i_l1~.~-~ 90 Four or more 75
The reduction in intensity of floor beam loads shall be determined as in the case of main trusses or girders, using the number of truck train loadings which must be used to produce maximum stresses in the floor beam.
2. 8- SIDEWALK, CURB, SAFETY CURB AND RAILING LOADING
A. Sidewalk Loading
Sidewalk floors, stringers, and their immediate supports, shall be designed for a live load of 85 pounds per square foot of sidewalk area. Girders, trusses, arches and other members shall be designed for the following sidewalk live loads per square foot of sidewalk area:
Spans 0 to 25 ft. in length Spans 26 to 100 ft. in length Spans over 100 ft. in length according
p ( 55~1iJ \ --l so !
85 lbs. 60 lbs.
to the formula
in >vhich
P live load per square foot (maximum, 60 lbs. per sq.ft) L loaded length of a sidewalk in feet W width of sidewalk in feet
In calculating stresses in structures which support cantilevered sidewalks, the sidewalk shall be considered as fully loaded on only one side of the structure if this condition produces maximum stress.
B. Curb Loading
Curbs shall be designed to resist a lateral force of not less than 500 pounds per linear foot of curb, applied at the top of the curb, or at an elevation 10 inches above the floor if the curb is higher than 10 inches. Where sidewalk, curb and traffic rail form an integral system, the traffic railing loading shall apply and stresses in curbs computed accordingly.
C. Safety Curb Loading
Safety curbs, or wide curbs provided for occasional use of pedestrians, shall be designed for loads specified in paragraph (A) if the curb is more than 2 feet in width. If 2 feet or less in width, no live load shall be applied.
D. Railing Loading
(1) Roadway Railings
Top members of roadway railings shall be designed to resist a lateral horizontal force of 150 pounds per linear foot together with a simultaneous vertical force of 100 pounds per linear foot applied at the top of the railing. When curbs are not less than 9 inches in height, lower rails shall be designed to resist a lateral horizontal force of 300 pounds per linear foot. 1iJhen curbs are less than 9 inches in height, this force shall be increased 40 pounds per linear foot for each inch the curb is less than 9 inches in height except that the adJed increment of horizontal force to be applied
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to the lmver railing shall not exceed 200 pounds. If there is no lower rail, the web members shall be designed to resist a horizontal force of 300 pounds per linear foot applied not less than 21 inches above the roadway. For each inch of height of curb above 10 inches this lateral horizontal force may be reduced 15 pounds per linear foot, but this force Ehall not be less than 150 pounds per linear foot. The horizontal forces shall be applied simultaneously. Railingi:' without webs and with single rails shall be designed for the forces specified above for low2r rails.
(2) Sidewalk Railings
Side\valk railings shall !:>e designed to resist the same forces as those specified for roadway railings, subject to the same restrict~ ions concerniHg curb heights. w11ere through trusses, girders, or arches separate the sidevwlk and road1vay or where side-walks are protected by curb railings, the sidewalk railings shall be designed only for the forces specified for the top rail.
2.9- IMPACT
Live load stresses produced by the standard Truck-Train loading shall be increased for i terns in Group A by allowance as stated therein, for dyuamic ,, 'Jibratory and impact effects. Impact shall not be applied to items in Group B.
(A) Group A
(1) Superstructure) including steel or concrete supporting columns, steel towers, legs of rigid frames and generally those portions of the structure >vhich extend down to the main foundation.
(2) The portion above the ground line of concrete or steel piles which are rigidly connected to the superstructure as in rigid frame or continuous designs.
(B) Group B
(1) Abutments, retaining walls, piers, piles, except Group A(2) (2) Foundation pressures and footings (3) Timber structure (4) Sidewalk loads (5) Culverts and structures having cover of 3 feet or more
(C) Impact Formula The amount of this allowance or increment is expressed as a fraction
of live load stress, and shall be determined by the formula:
I = 15
in which L + 20
I impact fraction (maximum 30 per cent) 1 length of span in feet
For uniformity of application the span length "V' shall be especially considered as follows:
For roadway floors, use the design span length. For transverse members, such as floor beams, use the span length of member centre to centre of supports, For computing truck load moments use the span length, except for cantilever arms use the length from moment ce.ntre to the farthermost axleo For continuous spans use the length of span under consideration for positive moment, and use the average of tvm adjacent loaded spans for negative moment. For bridges having cantilever acms with suspended spans, use the span of the cantilever arm plus half the length vf the suspended span when designing the cantilever and tti;:: span length of the suspended span designing the latter. For shear due to truck loads use the length of the loaded portion of span from the point under consideration to the far reaction.
For culverts with cover O' to 1! ~· O" inc, !=30~~ H II i'f li 1' 1'' to 2 I ~ on inc. I=20'1o II II !! 1! 2' 111 to 2' ~ llll inc. I=lO%
2. 10,·· LONGI'I'UDINt\L FORCES
Provision shall be made for longitudinal forces arising from any one. or more of the follmving causes~·
(a) Tractive effort caused through acceleration of the driving wheels or brak1ng effort from the application of the brakes to the braking wheels,
This force shall be equal to ;'30/~ of the >veigt1.t. of the vehicle or any portion of the vehicle on the loaded span, the truck loads in one lane only being considered. For military loading this force shall be equal to ~-57;of the weight of the military vehicle,
·The centre of gravity of this longitudinal force shall be assumed to be located 6 feet above the profile grade of the roadway slab,
, The change in the vertical reaction due to the transfer of the longitudinal force to the bearings 1 shall be accounted for.
(b) Frictional resistance offered to the movement of expansion bearings due to change of temperature or any other cause.
This force shall be equal to the dead load reaction multiplied by the coefficient of friction as shown below for the various
2-8
types of bearing:
For roller bearings For sliding bearings of hard copper alloy For sliding bearings of steel on cast iron or
0.03 0.15
steel on steel 0.25 For sliding bearingsof steel or ferro asbestos 0.20 For sliding bearings of concrete on elastomeric bearing pads 0.20
2 . 11- WIND LOAI1S
The follm..ring wind load forces per squa-re fov t of exposed area sh::!ll hE:, B()plied to all structures (sec Article\ 5.1 for percentage of basic unit ,sc.re;,;s ~:o he used uuder various combiru-1tions of loads and forces). The '"xposed Hrl?d considered shall he the sum of the areas of all members, i:lclud-:Lng fJ.oox system and railing, as seen in elevation at 90 degrees to the .Longitudinal axis of the structure. The forces and loads given herein are for a wind VBlocity of 100 miles per hour. For Group II loading, but not br Group III loading, they may be reduced or increased in the ratio of the square 0f the design wind velocity to the square of 100, provided the maximum probable wind velocity can be ascertained with a reasonable accuracy,or ':here .are permanent features of the terrain which make such changes safe and advisable. If change in the design wind velocity is made, the design •vtnd velocity shall be shown on the plans.
(A) Superstructure Design
A moving uniformly distributed wind load of the following intensity shall be applied horizontally at right angles to thefiongitudinal axis of the structure :Ln the design of the superstructure:·
For trusses and arches--,.c.-------------75 pounds per square foot For girders and beams --------------50 pounds per square foot
The total force shall not be less than 300 pounds per linear foot in the plane of the loaded chord and 150 pounds per linear foot in the plane of the unloaded chord on truss spans and not less than 300 pounds per linear foot on girder spans.
The above forces shall be used for Group II loading. For Group III loading there shall be added thereto a load of 100 pounds per linear foot at:plied at right angles to the longitudinal axis of the structure and 6 feet above the deck as a wind load on a moving live load. ~~en a reinforced concrete floor slab or a steel grid deck is keyed to or attached to its supporting members, it may be assumed that the deck resists within its plane, the shear resulting from the wind load on the moving live load.
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(B) Substructure Design
Forces transmitted to the substructure by the superstructnr-2 and forces applied directly to the substructure by wind loads shall be assumed to
be as follows:
(1) Forces from Superstructure
The transverse and longittldinal forces transmitted by the superstructure to the substructure for varying angles of wind direct -ion shall be as set forth in the following table" The skew angle is measured from the perpendicular to the longitudinal axis, The assumed wind direction shall be that which produces the maximum stress in the substructure being designed, The transverse a:1d longitudinal forces shall be applied simultaneously at the elevation of the centre of gravity of the exposed area of the superstructure.
Trusses Girders
Skew Angle Lateral Load Longitudinal l,at:eral Load Long it ud ina 1 of Wind per Sq, FL Load per sq. per Sqo Ft. Load per sqo (Degrees) of Area Fto of Area of Area Ft. of Area
(Pounds) (Pounds) (Pounds) (Pounds)
0 75 0 50 0 15 70 12 44 6 30 65 28 41 12 LJS 47 41 33 16 60 25 50 17 19
The loads listed above shall be used. in Group II loading as given in Article 5" 1
For Group III loading, these loads may be reduced 70 per cent and there shall be added thereto, as a wind load on a moving live load, a load per linear foot as given in the following table:
Skew Angle of Wind (Degrees)
0 15 30 45 60
Lateral Load per Lin, Ft. ( Pounds )
100 88 82 66 34
Longitudinal Load per Lin. Ft. ( Pounds )
0 12 24 32 38
"' This load shall be applied at a point 6 feet above the deck, "''
For the usual gird2r and slab bridges having maximum span
2-10
lengths of 125 feet, the following wind loading may be used in lieu of the more precise loading specified above.
\2)
W ( wind load on structure) SO pounds per square foot, transverse; 12 pounds per square foot, longitudinal. Both forces shall be applied simultaneously.
WL(wind load on live load) 100 pounds per linear foot, transverse;
40 pounds per linear foot, longitudinal. Both forces shall be applied simultaneously.
Forces applied directly to the substructure
The transverse and longitudinal forces to be applied directly to the substructure for a 100 mile-per-hour wind shall be calculated from an assumed wind force of 40 pounds per square foot. For >vincl direction assumed skewed to t.he substructure this force shall be resolved into component[.; perpendicular to the end and front elevations of the substructure according to the functions cf the skew angle. The component perpendicular to the end elevation shall act on the exposed substructure area as seen in end elevation and the component perpendicular to the front elevation shall act on the exposed substructure area as seen in front elevation. These loads shall be assumed to act on horizontal lines at the centres of gravity of the exposed areas and shall be applied simultaneously vJith the wind loads from the superstructure. The above loads are for Group II ~oading and may be reduced 70 per cent for Group III Loading.
(0) Overturning Forces
The effect of forces tendi>:tg to overturn structures shall be calculated under Group II and Group III of Article 5.1. An up1vard force shall be applied at the 1.vind•-vard quarter point of the transverse superstructure width. This force shall be 20 pounds per square foot of deck and sideT.valk plaa area for Group II combination, and 6 pounds per square foot for Group III combination. The wind direct ion shall be assumed to be at right angles to the longitudinal axis of the structure.
2.12- THER~~L FORCES
Provision shall be made for stresses or movements resulting from variations in temperature. The ri.se and fall in temperature shall be fixed for the locality in whL·h the structure is to be constructed and shall be figured from an assumed temferature at the time of erection. Due consideration shall be given to the lag between air temperature and the interior temperature of massive concrete members or structures.
2-11
The range of temperature shall generally be as follow
Metal Structures
Moderate climate from.0°to 120°F Extreme climate from minimum-30° F to 120° F
Concrete Structure Moderate Climate Extreme climate
Temperature Rise 30° F
'45°F
Temperature Fall 30°F
·'"""'45'0 F
2.13- UPLIFT
Provision shall be made for adequate attachment of the superstructure to the substructure should any loading or combination of loading, increased by 100% of the live load plus impact, produce uplift at any support.
2.14- FORCE OF STREAM CURRENT
(A) All piers and other portions of structures which are subject to the force of flowing water shall be designed to resist the maximum stress induced thereby.
The effect of stream flow on piers shall be calculated by the formula:
p KV2 where '
Pressure in pounds per square foot velocity of water in feet per second
p = v = K = a constant having the following values for different shapes
of piers
Square end piers Circular piers or piers with semi-circular ends Piers with triangular ends where the angle is 30 degrees or less Piers with triangular ends where the angle is more than 30 degrees but less than 60 degrees Piers with triangular ends where the angle is more than 60 degrees but less than 90 degrees Piers ends of equilateral arcs of circles Pier ends of arcs intersecting at 90 degrees
1. 50 0.66
0.50
0.50 - 0. 70
0. 70 - 0.90 0 .£~5 0.50
(B) The value of v2 in the equation P = KV2 shall be assumed to vary linearly from zero at the point of deepest scour to the square of the maximum velocity at H.F.L. The maximum velocity shall be assumed to be equal to 1.4 times the maximum mean velocity of the current.
(C) The intensity of pressure P, shall be applied to all portions of
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the pier extending above the point of deepest scour. This will include piles when a pile foundation is used.
(D) When the current strikes the pier at an angle, the velocity of the current shall be resolved into two components, one parallel, and the other normal to the pier. The value of the coefficient K to be applied to the component parallel to the pier shall be as per paragraph A of this article. The value of K to be applied to the component normal to the pier shall be 1.5 except for circular piers in which case the value will be 0.66.
(E) When piers are designed parallel to flow an allowance of a 20 degree oblique flow shall be included in the design.
2.15- BUOYANCY
Huoyancy shall be considered as it effects the design of either the sub~ structure, including piling, or of the superstructure.
'No provision need be made for buoyancy if the bridge is founded on hcmogeneo'JS, impermeable strata. For bridges founded on coarse sand or shingle, ful1 buoyancy shall be allowed. For other foundation conditions, including foundations on rock, the calculated effect o£ buoyancy may be taken as a fraction of the full buoyancy, at the discretion of the engineer responsible for the design.
2.16- EARTH PRESSURE
Structures which retain fills shall be proportioned to withstand pressure as given by Rankin 1 s formula; provided, however, that no structure shall be designed for less than an equivalent fluid pressure of 30 pounds per cubic foot.
For rigid frames a maximum of one~half of the moment caused by earth pressure (lateral) may be used to reduce the positive moment in the beams, in the top slab, or in the top and bottom slab, as the case may be.
\"''hen highway traffic can come within a horizontal distance from the top of the structure equal to one half its height, the pressure shall have added to it a live load surcharge pressure equal to not less than 2 feet of earth.
Where an adequately designed reinforced concrete approach slab supported at one end by the bridge is provided, no live load surcharge need be considered.
All designs shall provide for the thorough drainage of the backfilling material by means of weep holes and crushed rock, pipe drains, gravel drains, or perforated drains.
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2.17- EARTHQUAKE STRESSES
In regions where earthquakes may be anticipated, provlslon shall be made to accommodate lateral forces from earthquakes as follow:
where
EQ = CD
EQ Lateral force applied horizontally in any direction at centre of gravity of the weight of the structure.
D Dead load of structure
C 0.02 for structures founded on spread footings on material rated as 4 tons or more per square foot.
0.04 for structures founded on spread footings on material rated as less than 4 tons per square foot.
0.06 for structures founded on piles.
Live load may be neglected.
2.18- CENTRIFUGAL FORCES
Structures on curves shall be designed for a horizontal radial force equal to the following percentage of the live load, without impact, in all traffic lanes:
where c the s the D the R = the
c == o.00117 s 2 D 6.68 s2
R
centrifugal force in percent of the live load, without impact design speed, in miles per hour degree of curve radius of the curve, in feet
The centrifugal force shall be applied 6 feet above the roadway surface, measured along the centre line of the roadway. The desigil speed shall be determined with regard to the amount of superelevation provided in the roadway. The traffic lanes shall be loaded in accordance with the provision of Article 2.5 and 2.6
When reinforced concrete floor slab or a steel grid deck is keyed to or attached to its supporting members, it may be assumed that the deck resists, within its plane, the shear resulting from the centrifugal forces acting on the live load. The effects of superelevation shall be taken into account.
Section 3 - DISTRIBUTION OF LOADS
3.1- DISTRIBUTION OF HHEEL LOADS TC STRINGERS, I.DNGITUDINAL BEAHS AND FLCC'"R 3EAHS
(A) Position of Loads for Shea1
In calculating end shears a~d end reactions in transverse floor beams and longitudinal beams and str:i_ngers, no lateral or longitudinal distrihutioa of the ;,-Jheel load shall be assumed for the whee~ o-c axle load adjacent. to the end at which the stress is being determ~died. For lo.:ods in other positions on the span, the distribution for shear shall be determined by the method prescribed for moment.
(B) Bending Noment in Stringers and Longitudinal Beams
In calculating bending moments in longitudinal beams or stringers no longitudinal distribution of !:he wheel load shall be assumed. The lateral distribution shall be determined as follows:
(1) Stringers and Beams
The live load bending moment for each stringer shall be determined by applying to the stringer the fraction of a wheel load (both front and rear) determined by the following table:
Kind of Floor
Concrete:
On steel I-beam Stringers (a)
On concrete Stringers (c)
Concrete box girder (d)
Bridge Designed for one traffic lane
S/7.0 If s exceeds 1 ,, 1 v see note (b)
S/5.5 If s exceeds 6' see note (b)
S/8.0 If s exceeds 12' see note (b)
Bridge designed for two or more traffic lanes
S/5.5. If s exceeds 14' see note (b)
S/5.5 If s exceeds 14' see note (b) '' /:--;
S/7.0 If s exceeds 16' see note (b)
The dead load considered as supported by the outside roadway stringer or beam shall be that portion of the floor slab carried by the stringer or beam. Curbs, railing and wearing surface, if placed after the slab has cured, may be considered equally distributed to all roadway stringers or beams.
3-1
Notes:
S average stringer spacing in feet
(a) Design of I=Beam Eridge by N.M. Newmark-Proceedings, ASCE, March 1948.
(b) In this case the load on each stringer shall be the reaction of the wheel loads, assuming the flooring between the stringers to act as a simple beam .
. (c) Design of Slab an~ Stringer Highway Bridges by N.M.
Newmark and C. 2. C~ie:::;s~ Public Roads, January-:FebruaryMarch 1953.
(d) The sidewalk 1 iVt' load (see 2. 11) shall b2 omitted for interior and exterior box girders designed in accordance with the wheel load distribution indicated herein.
(2) Total capacity of Stringers
The combin~d design load capacity of all the beamb in a span shall not be le~:s than required to support the total live a~ .. d dead load in the span,
(A) Span Lengths ( See also Article 6.2 )
for simple spans the span lengU! shE-ill bP the distar"cce cec,tre c:o cc:ntre of supports but not to exceed clear span plus thickness of slab.
The following effective span lengths shall be used in calculating distribution of loads and bending moments for slab continuous O'.'er more th&n two supports:
Slabs monolithic with beams or walls (without haunches)
S Clear Span
Slabs supported on steel stringers
S distance between edges of flanges plus ~ of the stringer flange width
(B) Edge Distance of Wheel Load
In designing slabs the centre line of wheel load shall be assumed to be 1 foot from the face of the curb.
3-2
(C) Bending Moment
Bending moment per foot ~·7id~h o[ sJab shall be calculated according to methods given under Cases A and H.
In cases A and B:
S Effective span length, in feec, as defined under "Span Lengths" (Art. 3.2(A) and 6.2)
E Width of slab in feet over \vhich the load is distributd
P Load on one wheel of truck 12,500 pounds for Class A loading
7,500 pounds for Class B loading
Case - A Hain Reinforcement perpendicular to traffic The live load moment per foot width of slab for a simple span shall be determined by the following formula (Impact not included)
M (S+2) P/25
In slabs continuous over three or more supports a continuity factor of 0.8 shall be applied to the above formulas for both positive and negative moment.
Case - B Main Reinforcement Parallel to traffic For distribution of wheel loads
E 2+0.68
For roadway widths >- 28' :;;;-
K = 1
For roadway widths ~ 28'
K
7.0 1 X K
Roadway width
14 x Number of Truck Train Load -ings
Truck train moments for continuous spans and simple spans, except as noted, shall be determined by suitable analysis and distributed over a width of 2E. The lateral distribution of wheel loads for multi-beam precast concrete bridges shall not exceed that specified for slabs.
The live load-moment per foot width of slab for simple spans shall be determined by the following formulas.
3-3
(Impact not included)
For simple spans up to 35'
Use N == 0.9S X K
For simple spans 35' to 70'
Use H = (1.35 c ..:> - 16) X 1Z (Foot )~ips)
(D) Edge Beams ( Longitudinal)
Edge beams shall be provided for all slabs having main reinforcement parallel to traffic. The beam may consist of a slab se.ction adrlitionally reinforced, a beam integral with and deeper than the slab, or an integral reinforced section of slab and curb.
It shall be designed to resist a live load moment of
0.5 x simple span truck train Moment
Value for continuous spans may be reduced 20 per cent unless a greater reduction results from a more exact analysis.
(E) Distribution Reinforcement
Reinforcement shall be placed in the bottoms of all slabs transverse to the main steel reinforcement, to provide for the lateral distribution of the concentrated live loads, except that this specification will not apply on culverts or bridge slabs when the depth of fill over the slab exceeds two feeL The amount shall be the percentage ·:;Jf the main reinforcement steel required for positive moment as given by the follovJing formula:
For rnain rein.forcemer.;_t parallel to ':raffic;
100
.F'or :nr:~i:1 rei·nforce:rnent p icular to traffic:
::20
Where S = the 0ffective spa~ l~2grh, Lfi teet
~FOr rna. i.n rein for c ent£;·nt per pe-c1f.i i c u la t· Lo t r s. f f i ~ th ~~ s pe-e· if Led ctJnou n ~.:: o.t
distribution reinforc.ern,=::nt sl:all bt~ us2d i the rntddle half of the spc.n but t~Il_i.~
may be reduced by 50% in the end quarLers of the span. Longitudinal reini:orcement. in tLe top of slab ha,Jing ti:H' main
reinforcement perp,:>nd icu1ar ro traffic shall not be les:~ rhail 0, 20 square inch per foot of widt:h.
(F) Shear and Bond stress in Slabs
Slabs desi~ned for benrlin~ moment in accordance with the foregoing shall be considered satisfactory in bond and shear.
(G) Unsupported Edges, Transve:·se
The design assumptions of ... his article do e10t pro'Jide for the effect of load near unsupported ·c::dges. There fore, at the ends of the bridge and at intermediate points ';~here the continuit.y of the slab is broken, the edges shall be suprcrted by diaphragms or other suitable means. The diaphragms shall be designed to r2sist the full moment and shear produced by the wheel loads which can come on them.
(H) Cantilever Slabs
Under the following formulas for distribution of loads on cantilever slabs, the slab is designed to support the load independent of edge support along the end of the cantilever.
Case A. Reinforcement Perpendicular to Traffic
Each wheel on the element perpendicular to traffic shall be distributed according to the following formula:
E o.6x+2.5 PX
Moment per foot of slab = -E
in which X = distance in feet from load to point of support
Case B. Reinforcement Parallel to Traffic
The distribution for each wheel load on the element parallel to traffic shall be as follows:
E 1.2X + 1.6 E 7.0 X K max
For roadway widths ~ 28' K= 1
For roadway widths <28' Roadway width K=
14x Number Truck Train Load in
In calculating the moments one axle load of 36000 lbs. may be substituted for the two 25000 lbs tandem axles of the standard truck train if this produces a greater stress.
3-5
(I) Slab Supported on Four Sides
In the case of slabs supported alo~:tg four edge;o. and reinforced in both directions the proportion of the load carried by the short span of the slab shall be assumed as gi'Jen by the follmving equations:
b4 For load uniformly distributed, p
a4 + b4
b3
For load concentrated at centre,p a3 + b3
i\fhere p proportion of load carried by short span a = length of short span of slab b length of long span of slab
Where the length of the slab exceeds 1~ times its width, the entire load shall be assumed to be carried by the transverse reinforcement.
The distribution \vidth, E, for the load taken hy either span Bhall be determined as provided for other slabs. Moments obtained shall be used in designing the centre half of the short and long slabs. The reinforcement steel in the outer quarter of both short: and long spans may be reduced 50 per cent. In the design of the supporting beams, cons ideratio•1 shall be given to the facr that the loads rle}h!ered to thE· supporting beaws are not uniformly distributed along the beams.
3. 3- DISTRIBUTION 01: lrT!:lt<:E1~ l.OPI.DS T!:lR01!GFi EAR'f!-1 .FILLS
Whe!t the depth of fill is 2 fe;~t or more, conceEtrated loads shal i he considered as uniformly distributed over a square, the sides of >:vhich an: equal to 1-3/4 times the depth of fill.
'i.l!e shear produced by such loads shall be calculated as provided for dead loads.
When such areaa from several concentrations overlap, the total load shall be considered as uniformly distributed over the area defined by t:he outside limits of the individual areas, but J:h.e tota1 vJidth of distrihnion shall nor exceed the total width of the supporting slab. For single span the effect of live load may be neglected when the dept.h of fill is more tlH:trl 8 feet and excec.;ds the span length; for nmltipl2 spans it may be neglected ,,Jhen the depth of fill exceeds the distance bet\veen races of enJ supports or abutments. When the depth of fill is less than 2 feet the 1-iheel load shall be distributed as in slabs with concentrated loads. V.Jhen the calculated live load and impact moment in co::1crete slabs based on distribution of the wheel load through fills· as herein outlined exceeds the live load and impact momen! calculated according to Article 3.2 then the latter moment shall be used.
3-6
Section 4- l-'l.ILITARY LOADING
4.1- LOADING
1':'1e military loading on the roadways of bridges or incidental structures shall consist of 70 long ton tracked vehicle as shown in Figure 5 subject to the restriction that the nose to tail distance between two successive vehicles is not less than 300 feet. No other live load shall cover any part of the roadway of the bridge when this vehicle is crossing the bridge. Only one such train shall occupy the roadway of the bridge.
..... ~
"' " v v co 00 ,.._ ,.._
-0 (/) (/) I
z z -C\1
~ 0 1-
10 1n J'() J'()
70 TON MILITARY LOADING
FIGURE 5
4-1
HORIZONTAL CLEARANCE
The minimum clearance betweec-1 th2 rc.advn:;.y i;:;.ce o"" ctcrb and the outer edge of ch2. track shall be assumf'd aH tollo"'rs ~
\..Jid th ot roadway
4,3=
11 1 -6 1; to 13' ~6<1--====•c•===== 13 '-6! 1 to 18 '-0''=====-==~~~
1'-0" 2'=0 11
4'·~0n
Unless a more exact annlysis is made the 70 T ~1ilitary L:J&d shall be distributed to the stringers as indicat;;:d ':ielow~
4.4- IMPACT
Live load stresses shall be increased for items in Group AJ n,,ferred to in Article 2.9 by an allowance as stated herein, for dynamic vibratory and impact effects.
Impact shall not be applied to items in group B referred to in article 2.9.
A, Impact Formul§J:.
4.5-
(A)
1. Concrete Structures
Spans less than 30 feet Spans 30-150 feet Spans greater than 150 feet., ,
2. Steel Structures
Spans less than 30 feet All spans greater than 30 ft ••
DISTRIBUTION OF LOADS AND DESIGN OF CONCRETE SLABS
Span lengths See Art. 3.2
(B) Edge distance of track
25% 10/~
8. 8/o
25% 10/o
In designing slabs the center line of track shall be assumed to be minimum 1'-6" from the face of curh,
4-2
(C) Bending Moment
B..::r::ding moment per foot of -;,d.d::J·; or s:c;.b sha.lJ. be calcDlat2c~ according to methods give.n nnder Ca.se':; A and B,
In cases A and B:
s E~fective span length ~n feet, as defined under "~)pan Length (Article 3,2.)n
E Width of slab in f6et over which a track is di~tributed
P Load on one track = 78.4 Kips (35 Long tons)
Case A - Hain Reinforcement Perper1dicular to 'iraffic
Moment for simple spans L 1 s
For spans continuous ·over three or more supports use 0,.8 x simple span moment for both positive and negative moment.
Case B :Main Reinforcement Parallel to Traffic
For simple spans greater than 12 feet
M P(S-~6) /I..~E
For simple spans less than 12 feet
For moments in continuous spans a suitable analysis shall be used. The width of distribution, E, shall be computed as follows:
.458 + 4.0
4-3
Section 5 -· UNIT STRESSES
5.1 GENERAL
Unless otherwise noted the allowable unit stresses indicated herein are given in pounds per square inch.
The following groups represent various combinations of loads and forces to which a structure may be subjected. Each part of such structure or the foundation on which it rests, shall be proportioned for all combinatio~s of such of these forces as are applicable to the particular site or type, and at the percentage of the basic unit stress indicated for the various groups except that no increase in allowable unit stresses §.lJ..aJLb.e perglitted for members or conn~-~tions carrying wind loads oniy. See article 2.1 to 2.l8 fOr 'Toads. and forces.
The maximum section required shall be used.
Group I Group II Group III Group IV Group v Group VI Group VII Group VIII Group IX
'.D IL l
/I 'E ;B
w WL
..;,{"'' ". :..~l<"'\#8~>1'11~
D+L+I+E+B+SF D+E+B+SF+W , ...
' . ....-~ .·/. ;; "·~- . ~--··-,;· . Group I+b.~+F-1-CF+~p% ~;2-!!,&i'
== Group I+R+S+T .. - ...... · Group II+R+S+T
= Group III+R+S+T - D+E+B+SFilEQ} == Group I+fcE == Group II+ICE
Dead Load = Live Load
Live Load Impact / (, = Earth Pressure
Buoyancy == Wind Load on Structure
Wind Load on Live Load-100 pounds per linear foot
LF = Longitudinal Force from Live Load CF = Centrifugal Force F Longitudinal Force due to friction R Rib Shortening S Shrinkage T == Temperature EQ Earthquake SF Stream Flow Pressure ICE Ice pressure
5-1
Percentage of Unit Stress
100% ··125% 125% 125% 140% .140% 133% 140/o 150%
r I
5.2- CONCRETE STRESSEs(i)
(A) Standard Notations and Assumptions
f 1 c
::::
fc = Permissible Extreme fiber stress in compression
f 1 c Unit ultimate compressive strength of concrete. as determined by 6 inch cube tests ar: 28 days,
(f'c) == Unit ultimate compressivE: strength of concrete as determined by 6" cylinder test at 28 d::tys.
n ratio of modulus of elasr.icity of steel to that of concrete. The 'value of n, as a function of the ultimate strength of cone:. rete, shall be assumed as follows:
Cube Cylinder
2600 3100 (f'c) = 2000 2400 n=l5 3200 3700 2500 - 2900 n=l2 3800 5000 3000 = 3900 n=lO 5100 5.'·900 4000 = 4900 n= 8 6000 or more 5000 - or more n= 6
for computations of deflections the value of n=8 shall be used.
Coefficients:
Thermal Shrinkage.
.000006 ,0002
per
(B) Allowable Stresoes (ii)
(1) :flexurco. Extreme fiber in compression. Extreme fiber in tension 0
plain concrete, primarily in footings-------------------= Extr·.::me fiber in tension,. reinforced concrete---------
Cube Strength
fc= 0.33 f'c
ft:= 0,025 f'c
None
Cylinder Strength 0.40(f'c)
O.OJ(:Cc)
None
The ratios and --:,ralues in thiB SE,ction apply to concrete made with convef1t -ional hard rock aggregate, values applicable to light weight aggregate concrete should be established by adequate investigation,
(ii) In no case shall the allowable stresse.s be basE:d on an ultimate cube strength greater than 5800 psi or ultimate cylinder strength greater than 4500 psi except for prestressed concrete.
5-2
(2) Shear
Beams without web reinforcement Longitudinal bars not anchored or plain concrete footings----
Longitudinal bars anchored
Beams with web reinforcement
Horizontal shear in shear keys between slab and stem of T beams and box girders
Cube Strength
0.016 f'c
0.024 f'c
V=0.060 f'c bjd
0.12 f'c
Cylinder Strength
0.02(f'c)
Max 75 psi
0.03(f'c) Max 90 psi
0.075(f'c)bjd
O.lS(f'c)
(3) BonJ, Deformed bars:
5 ,, ',)=
With deformation complying with specifications ASTM A 305 Straight or hooked er:ds,exclus= ive of top bars
(a) In beams, slabs, o~e way footiu.gs,
(b) In two w.TJ footingt: B(;'Y, of mw ;,1ay footi.Tt>U'
Top bars= Hsrs t1F:ar top o~: b?BElS
and gird·:;rs having more thBn 12
0.08
inches of concrete under th8 bar2 0.05 f 1 c
0.10(£' c)
0.06
For plain bars the VBll1fcS list:nd ior defonued bB.rs sh,;ill be d.ecn,ased by 5W,
REINFORCJ<:MFNT
Nild Steel co;:tforming to -!LS, 785 or A3'i'H A15 ~)peci:ficHtionR
SteP.l P.e:Lnforcement:
Tens ion in flexural nerr!bersc" ------ ··-- --18,000 Te::~s ioD in web men1aers~ --- -·-- ~ -~·--~- --18, 000 Compress ior1 in co lum::::.s~ -- ---=---- -----13 ~ 200 Co;!ipression in be;;tr:lS See Article 6. 6
5.4= SIEE~ STRESSES
Parr: Steel
3 B, stre~>SE-s
Stresses, shall conforn, to the British ;Jesign Sta:1{'iard 153 of the British Standard Institution 1958 Edition.
5-3
SECTION 6 - CONCRETE DESIGN
6.1- GENERAL ASSUMPTIONS
The design of reinforced concrete members under these specifications shall be based on the following assumptions:
(1) Calculations are made with reference to unit working stresses and safe loads, as elsewhere specified herein, rather than 1iJith reference to ultimate strength and ultimate loads.
(2) A plane section before bending remains plane after bending.
(3) The modulus of elasticity of concrete in compression is constant within the limits of working stresses; the distribution of compressive stress in flexure is, therefore, rectilinear.
(4) The ratio 11n" shall be assumed as follows:
Value of n
Ultimate strength of concrete, Lbs. per sg.in. 611 cube 6 11 cylinder ]trength strength
2600 - 3100 3200 3700 3800 - 5000 5100 - 5900 6000 or more
2000 - 2400 2500 2900 3000 - 3900 4000 - 4900 5000 or more
Es
Ec
For computations of strength
15 12 10
8 6
For computtation of deflection
8
In computing the ultimate deflection of slabs and beams, the value of the modulus of elasticity should be assumed as one-thirtieth that of steel in order to allow for the effect of plastic flow and shrinkage.
(5) Concrete shall be assumed as offering no tensile resist-ance.
(6) The bond between concrete and metal reinforcement is a.s;:;umed to remain unbroken throughout the range. of working stresses. Under compression the two materials are therefore stressed in proporation to their moduli of elasticity.
(7) Initial stress in the reinforcement due to contraction or expansion of the concrete, is neglected, except in the design of reinforced concrete columns.
6-1
(8) For the determination of external reactions, moments, shears, and deflections, moments of inertia of rigid frame and continuous structures shall be computed for the gross concrete sections, neglecting the effect of steel reinforcement, except that the transformed area of the steel 3hall be included for columns, arches or other compressive members.
(9) 1be moment of inertia of the entire superstructure sections, except railings or any curbs or sidewalks not placed monolithically with the superstructure before the falsework is released, and the moment of inertia of the full cross section of the pier or bent shall be used to determine the elastic properties of the various spans-and supports.
(10) The depth of girder or L~lab to be used in computing momer1t of inertia at the centerline of the support shall be ohtair1ed by extending the slope of the intrados of the member to the centerline.
(11) Rigid frames ahall be considered free to sway longitudinally due to the application of vertical dead loads and vertically applied live loads except when the structure is restrained from movement by extertEll forces.
(12) The assumption of no moment restraint at the base of column shall be m<'3d in the analysis of rigid fra:nes (superstructures) unlsss the bas~=: is knmvn to be fully fixed. When a pim!ed end condition is assumed for the analysis of the superstructure, the base of column, footing and piling shall be designed to resist the mor.1ent resulting from a!l a2sumed restraint varying from zero to full fixity. The degree of restraint shall he deterrt1i.ned by the type of footing and the character of the foundation material.
(13) Piers or bents constructed integrally with footings placed on a skew exceeding 10° shall be considered fixed at the top of footing.
6.2- SPAN LENGTHS
The effective span lengths of slabs shall be as specified in Article 3. 2.
The effective span length of freely supported beams shall not exceed the clear span plus the depth of beam.
For the analysis of all rigid frames, the span lengths shall be taken as the distance between the centres of bearings at the top of th12 footings.
The span length of continuous or restrained floor slabs and beams shall be the clear distance between faces of support.
6.3- EXPANSION
In general, prov~s~on for temperature changes shall be made in all simple spans having a clear length in excess of 40 feet.
6-2
In continuous bridges, prov~s~ons shall be made in the design to resist thermal stresses induced or means shall be provided for movement caused by temperature changes.
Expansion not otherwise provided for shall be provided by means of hinged columns, rockers, sliding plates or other devices.
6.4- T-BEAMS
(A) Effective Flange Width
In beam and slab construction, effective and adequate bond and shear resistance shall be provided at the junction of the beam and slab. The slab may then be considered an integral part of the beam, but its assumed effective width as a T-beam flange shall not exceed the following:
(1) One fourth of the span length of the beam. (2) 1he distance centre to centre of beams (:3) Twelve time the least thickness of the slab plus
the width of the girder stem.
For beams having a flange on one side only, the effective overhanging flange width shall not excet.~d one twelfth of the span length of the beam, nor six times the thickness of the slab, nor one half the clear distance to the next beam.
(B) Shear
The flange shall not be considered as effective in computing the shear and diagonal tension resistance ofT-beams, except in the determination of the value of j.
The horizontal shearing unit stress at the juncture of the. flange and the monolithic fillet joining it to the girder stem shall not exceed that given in Article 5.2(B)(2), shear of beams with web reinforcement.
(C) Isolated Beams
Isolated beams, in which the T-form is used only for the purpose of providing additional compres:::io::1 area, shall have flange thickness of vot less than one-half the width of the web, and a total flange width of not more than 4 times the width of web.
(D) Diaphragms
For T-beam spansJdiaphragms or spreaders shall be placed between the beams at the middle or at the third points.
6-3
(E) Construction Joints
When a construction joint is required between the slab and the seem of the beam, the shear-keys shall be designed in accordance with allowable stresses given in Article 5.2(B)(2).
6.5- REINFORCEMENT
(A) Spacing
The minimum spacing centre to centre of parallel bars shall be 2~ times the diameter of the bar, but in no case shall the clear distance between the bars be less than 1~ times the maximum size of the coarse aggregate.
(B) Covering
The minimum covering, measured from the surface of the concrete to the face of any reinforcement bar, shall not be less than 2 inches except in slabs where the minimum covering shall be 1 inch at the bottom and P2" at the top. Where an additional wearing surface is to be used the required clearance at the top of slab may he reduced to 1". In the footings of abutments and retaining walls and in piers the minimum covering sh<:tll be 3 inches. In work exposed to the action of sea water the minirlmm covering shall be 4 inches except in precast concrete piles 3 where a minimum of 3 inches may be used. For stirrups in T-beams, the minimum cover shall be. 1~ inches.
(C) Splicing
Tensile reinforcement shall not be spliced at points of maximum stress. When reinforcement is spliced, the spliced bars shall lap sufficiently to develop the full strength in bond.
(D) End Anchorages and Hooks
End anchorage may be an extension of the bar, either straight, bent or hooked. A properly dimensioned hook is: (a) one in wb.ich the bar is bent: in a complete semi-circular turn with a radius of bend on the axis of the bar of not less than three bar diameters, plus an extension at the free end of at least four bar diameters?(b) a 90° bend having a radius of not less than four diameters plus an extension of twelve bar diameters.
Hooks having a radius of bend of more than six bar diameters shall be considered as extensions to the bars. Hooks shall not be considered effective in adding to the compressive resistance of bars. Any mechanical device capable of developing the strength of the bar without damage to the concrete may be used in lieu of hooks or extensions.
(E) Extension of Reinforcement
(1) To provide for contingencies arising from unanticipated distribution of loads, yielding of supports, shifting of points of inflection, or other lack of agreement with assumed conditions governing the design of elastic structure, the reinforcement shall
6-4
be extended at the supports and at other points between the supports as indicated in (2) to (5) below. These paragraphs relate to ordinary anchorage and are the minimum requirements under which normal working stresses for bond or shear are permitted.
(2) Negative tensile reinforcement at the supported end of a restrained or cantilever beam or member of a rigid frame shall be extended in or through the supporting member in such a manner as to develop the maximum tension in the bar with a bond stress not exceeding the normal working stress provided in Article 5.2.
(3) Between the supports of continuous or simple beams, every reinforcement bar shall be extended at least 25 diameters but not less than 1/20 of the span length, beyond the point at which computations indicate it is no longer needed to resist stress .A i!-typ•:o hcok si:1al1 be: co:.~sidered equal tc' 16~ and an I, type hook equal to s-,. (4) In simple beams and freely supported ends of continuous beams, at least 1/3 of the positive reinforcement shall extend beyond the face of the supports a distance sufficient to develop ~ the allowable stress in the bars.
(5) In restraiued or continuous beams at least i; of the positive reinforcement shall extend beyond the face of the supports and the remainder treated as provided in (3).
(6) Dowels and bars carrying little or no theoretical stress should be embedded at least ten bar diameters from the construction joint.
(F) Maximum Sizes
lbe maximum size of bar reinforcement shall be 1~ inches in diameter, unless the particular conditions warrant the adoption of special reinforcement design.
When structural steel shapes are used for reinforcement, mechanical bond should be provided which will effectively bond the memher to the surrounding concrete mass.
(G) Position of Negative Moment Reinforcement in I-Beams
Wben the floor slabs or flange of a continuous or cantilevered T-beam is placed after the concrete in the stem has taken its set, at least 10 per cent of the negative moment reinforcing steel shall be placed in the beam stem in order to prevent cracks from falsework settlemert or deflection. 'This reinforcing steel shall extend a distance of one-fourth the span length each side of t:he intermediate supports of continuous spans, one-fifth the span length from the restrained ends of continuous spans, and tte entire length of cantilever spans .In lieu of the above requiremer:.t two number
6-5
8 bars full length of the girders may be used
(") n Reinforcement of Beam Sides
The depth of the beam between the main reinforcement and the flange or the top reinforcement shall be reinforced with horizontal bars in both faces to prevent temperature and shrinkage cracks. The total area of steel in each face shall not be less than\ eq. in. per foot of height of the unreinforced beam side. The spacing of bars shall not exceed 2 feat.
6.6- COMPRESSION REINFORCEMENT II~ BEAMS
Compression reinforcement in girders and b~ams shall be secured against buckling by ties or stirrups adequately anchored in the concrete, and spaced not more than 16 bar diameters aparL Where compression reinforcem~nt: is used, its effective;:-~.ess in resisting bending ma:Y' be tc:~ken
as twice th~ ·.;alue indicated from the calculations as3uming a straigh t-1 ine relation between stress and strain and the modular relatio~ of stress in steel to stress in concrete given in Article 6.1(4). However, in no case should a str~ss in compression reinforcement gr2ater than 16,000 pounds per square inch be allowed.
6.7= WEB REINFORCEMENT
(A) Gt:c.neral
When the allowable unit shearing 3tres& for concrete is exceeded, web reinforcement shall be provided by one of th<::: following methods:
(1) Longitudinal bars bent up in s0ries or in single plane. (2) Vertical stirrups. (3) Combination of bent-up bars a:<1d vertical stirrups.
Wh.er1 any of the above methods m: reinforcement are used, tb.e concrete may be assumed to carry external vertical shear not to exceed .024 f' (cube strength) or . 03 (f~), (cylinder strength) (Maximum 90 pounds per sq~are inch) the remainder of shear being carried by the web reinforcement.
The we~s of T-beams and box girders shall he reinforced with stirrups in a 11 cases,
(B) Calculation of Shear and Bond
Diagonal tension, shear, and bond iQ reinforced concrete beams shall be calculated by the following formulas:
NOTATIONS:
A total area of web reinforcement in tension within a distance 11 s 11
v
6-6
b
d
j
s
u
v
V'
FORMULAS:
(measured in a direction parallel to that of the main reinforcement), or the total of all bars bent up in any one plane.
width of beam.
effective deptl-1, or depth from compression surface of beam to centroid of tension reinforcement.
tensile unit stress in web reinforcement.
ratio of lever arm of resisting couple to depth ;;d".
spacing of web reinforcement bars, measured at the neutral axis in a direction parallel to that of the main reinforcement.
bonJ stress per unit area of the surface of the bdr.
shearing unit stress
external shear on any section after deducting shear carried by concrete.
sum of perimeters of bars
angle between web bars and axis of beam
Shearing unit stress, as a measure of diagonal tension
v v bjd
Stress in vertical web reinforcement
f v
V' s
When a series of web bars of bent-up longitudinal bars are used, the reinforcement shall be designed by the following formula:
V' s
fv jd ( sinO:+ coso()
When the web reinforcement consists of bars bent up in a single plane so as to reinforce all sections of the beam which require reinforcement, the bent-up bars shall be designed by the following formula:
6-7
A V'
f sino( v
1be bond between concrete and reinforcing bars in beams and slabs shall be computed by the following formula:
v u
jd ~0
(For approximate results 11 j 11 in the above formulas may be taken as 7/8)
Bond shall be similarly computed on compressive reinforcement, but the shear used in computing the bond shall be reduced in the ratio of the compressive force assumed in the bars to the total compressive force at the section. Anchorage shall be provided by embedment past the Bection to develop the assumed compressive force.
(C) Bent-up Bars
Bent-up bars used as web reinforcement may be bent at any angle between 20 and 45 degrees with the longitudinal reinforcement. The radius of bend shall not be less than 4 diameters of the bar.
The spacing of bent-up bars shall be measured at the neutral axis and in the direction of the longitudinal axis of the beam. l'his spacing shall not exceed thre.:~~fourths the effective depth of the beam. The first bar from the support shall eros~ the mid-depth of the heam at a distance from thE face of the support, measured parallel to the longitudinal axis of the beam, not greater than one=half the effective depth.
(D) Vertical stirrups
Where stirrups are required to carry shear, the maximum spacing of vertical stirrups shall be limited to !;z the depth of the beam, and where not required to carry shear, the maximum spacing shall be limited to 3/4 the depth of the beam. The first stirrup shall be placed at the distance from the face of the support not greater than one- fourth of the effective depth of the beam.
(E) Anchorage
(1) The stress in a stirrup or other web reinforcement shall not exceed the capacity of its anchorage in the upper or lower one-half of the effective depth of the beam.
(2) Web reinforcement which is provided by bending into an inclined position one or more bars of the main tensile reinforcement where not required for resistance to positive or negative bending, may be considered completely anchored by continuity with the main tensile reinforcement, or by
6-8
embedment of the requisite length in the upper or lower half of the beam provided at least one half of such embedment is as close to the upper or lower surface of the beam as the requirements of fire and rust protection allow. A hook placed close to the upper or lmver surface of the beam may be substituted for a portion of such embedment.
(3) Stirrups shall be anchored at both ends by one of the following methods or by combination thereof: '
(a) Rigid attachment, as by welding, to the main longitudinal reinforcement.
(b) Bending round and clostly in contact with a bar of the longitudinal reinforcement, in the form of a U-stirrup or hook.
(c) A hook placed as close to the upper or lower surface of the beam as the requirements of fire and rust protection will allow. In estimating the capacity of this anchorage the stress developed by bond between midheight of the beam and the centre of bending of the hook may be added to the capacity of the hook.
(d) An adequate length of embedment in the upper or lower onehalf of the effective depth of the beam, whether straight or bent. Anchorage of this type alone should not be relied on for stirrups in cases where the shearing stress in the web exceeds that recommended for beams without end anchorage of the reinforcement.
(See Article 5.2)
6.8- COLUMNS
(A) General
Other provisions of Section 6, Concrete Design, shall apply in the design of columns unless specially modified by this article.
In the design of columns the unsupported length shall be defined as the clear distance between struts, cross beams, footings or other types of adequatE restraint to lateral movement. Where a bracing member has haunches at its junction to a column, the unsupported column length shall be measured from the junction of the haunch with the column provided that the face of the haunch makes an angle with the face of the column of at least 45 degrees.StrutE or cross beams joining columns at angles greater than 30 degrees from the plane of symmetry of the column shall not be considered as adequate support.
6-9
The least lateral dimension of a column shall be taken as: (1) for rectangular columns, the over-all thickness along a principal axis; (2) for spirally reinforced columns, the overall diameter including the encasement of the spirals; (3) for HT11 -shaped columns, the width or depth of the T.
In a column which, for archic:ectural or other reasons, has a larger cross section than required by the load carried, the minimum amount of longitudin::tl steel hereinafter specified may be reduced provided that in no case shall less 'longitudinal steel be used than that: required by the mir:imum column designed with one per cent of longitudinal steel.
The notations used in this article are as follows:
over~all or gross cross-sectional area of spirally reinforced or tied pier, pedestal or column in square inches.
cross-sectional area of core of spirally reinforced columns measured to the outside diameter of the spiral, square inches.
As = cross-sectional area of longitudinal steel
A Ag + (n-1) As , effective area of column
fa c or
0.30 f'c*
fa factor used in the design of members subject to combined axial and bending stresses
d least lateral dimension of column, inches
e eccentricity of resultant load on a column, measured from a gravity axis.
f'c = crushing strength of 611 cubes at age of 28 days, psi
(f'c)= crushing strength of 6"xl2" cylinders at age of 28 days, psi .
.J.
0.175 f~" + fs p fa for spiral columns and
1 + (n-1) p 80% of that amount for
0.225(f'c) + fs p tied columns. or
1 + (n-1) p
fe maximum allowable compressive stress in members subjected to combined axial and bending stress, psi.
fs nominal working stress in longitudinal reinforcing steel (see Article 5.3)
6-10 * 6" cube strength 'ld~ 6 11 cylinder strength
f's yield stress of spiral reinforcement (for steel grades not having a definite yield point, the str~ss causing a 0.2 per cent plastic set), psi
K
L n Pe Pp Ps Psl Pt Ptl p pi r
t
=
t 2 a factor used in the design of members subjt:cted to combined axial and bending stress.
unsupported length of column, inches. ratio of modulus of elasticity of steel to that of concrete. a load eccentrically applied. total load on pier or pedestal, pounds total load on spirally reinforced column, pounds total load on spirally reinforced long columns pounds total load on tied column, pounds total load on tied long column, pounds ratio of longitudinal steel area to gross column area ratio area of spiral reinforcement to core area radius of gyratio!l of section (transformed section) in the direction of eccentricity or bending. over=all depth of column in the direction of eccentricity or bending
(B) Piers and Pedestals
The ratio of the unsupported length of unreinforced concrete piers or pedestals to their least dimension shall not exce~d 3, The total load on any unreinforced concrete pier or pedestal shall not exceed that give.n by the following formula:
Pp 0.20 Ag f'c*
or 0.25 Ag (f'c)** (1)
(C) Spirally Reinforced Columns
(1) Longitudinal Reinforcement
Longitudinal reinforcement shall be placed within the area contained by the spiral reinforcement. The ratio between the area of longitudinal reinforcement and the gross area of the column, including the encasement outside: the spiral reinforcement, shall be not less than 0,01 nor more than 0.08. The:re shall be a minimum of six longitudinal bars evenly spaced around the periph-ery of the column core. The clear spacing between individual bars or pairs of bars at lapped splices shall be not less than 1~ inches or 1~ times the maximum size of the coarse aggrt>gate used, subject to the further requirement that the centre-to-centre spacing shall be not less than 2~ times the diameter of bars. The diameter of bars shall be not less than five-eighths inch. For columns with a
6-11 ~': 6" cube strength ** 611 cylinder strength
circular spirally reinforced core having excessive size or other outside shapes, the gross area to be used in determining percentage of reinforcement shall be a circle with a diameter equal to the minimum core required for structural design plus the specified outside cover.
(2) Spiral Reinforcement
Spiral reinforcement shall consist of uniform spirals held firmly in position by attachment to the longitudinal reinforcement. Spiral reinforcement may be plain ar deformed reinforcing hars or cold drawn wire. Splices in spiral bars should be avoided if practical and, if necessary~ shall be made by welding or by lap of 1~ tu-rns. The pitch of spirals shall not exceed 1/6 of the core diameter, The clear distance between individual turns of the spiral shall not exceed 3 inches or be less than 1-3/8 inches or 1~ times the maximum size aggregate used. Spiral reinforcement shall exte;:·:d from the footing or other support to the lEvel of the lowest horizontal reinforcement of members supported by the column.
The ratio of the volume of spiral reinforcement to the volume of core of the column, out to out of spirals, shall be not less than
'{(
(~ -1) f'c
Ac f's (2)
p1 0. 35
.. 1:-,-c
or 0,45 (~ -1) (f'c)
Ac f's
The yield strength for design assumption, f's shall not be taken higher than 60,000 p.s.i.
(3) Allowable Load ·· Short Columns
The provision of this subarticle shall apply only to columns having ratios of unsupported height to least lateral dimension of not more than 10. The total axial load on a column shall not exceed that given by the following formula.
"'k p 0.175 f'c Ag + As fs s 'i.(* (3)
or 0.225 (f'c) Ag +As fs
(4) Long Columns
The total axial load on a column having a ratio of unsupported height to least lateral dimension greater than 10, but not greater than
~'( 6"cube strength *i~ 611 cylinder strength
20, shall be not greater than given by the following formula:
Psl ~ Ps (1.3-0.03 L/d) (4)
If L/d ratio of columns exceeds 20, the column shall be investigated for elastic stability.
(D) Tied Columns
*
(1) Longitudinal Reinforcement
The longitudinal reinforcement shall consist of at least four bars, and when only four bars are used • they shall be placed at the corners of the section. Bars shall be placed at each intersection of column faces. The bars shall be not less than fiveeighths inch in diameter. The ratio of the total cross-sectional area of the bars to the total cross-sectional area of the column shall be not less than 0.01 nor more than 0.04.
(2) Hoops and Lateral Ties
Hoops shall surround the longitudinal reinforcement:. The·y shall be not less than one-fourth inch in diameter and shall be spaced not more than 12 inches apart except that this spacing may be increased in the case of pier shafts or columns having a larger eros& section than required by conditions of loading, Adequate auxilLe.ry ties shall be provided to support intermediate longitudinal bars whose distance from any tied bar exceeds 2 feet.
(3) Allowable Load - Short Columns
The provisions of this subarticle shall apply only to columns having ratios of unsupported height to least lateral dimension of not more than 10. The total axial load on a column shall be not greater than 0.8 of that given by equation 3, which results in
* p ~ 0.8 (0.175 f' A + A t -· c g s
or 0.8 (0.225 (f'c)-Jd; Ag + As
fs) (5)
fs)
(4) Long Columns
The total axial load on a column having a ratio of unsupported height to least lateral dimension greater than 10 but not greater than 20 shall be not greater than given by the following formula
Ptl = Pt (1.3-0.03 L/d) (6)
6-13 6" cube strength 6" Cylinder strength
If the L/d ratio exceeds 20, the column shall be investigated for elastic stability.
(E) Bending Moments in Columns
When beams or slabs are connected to columns; the moments induced in the columns by such beams or slabs shall be provided for in the column design.
(F) Combined Axial and Bending Stress
A reiaforced concrete column which is syrru.'1letrical about two mutually pe.rpendicular planes through its axis and wh.ich is subjected to an ax.i.al load f't>. s combi!ted with bendi:J.g in one or both o:i: the planes of syrn1netry may he designed on the basis of uncracked sections provided the ratio of eccentricity to depth e/t, is not greater than 0.5 in either plane, ·:r:he combined fiber stress in compression is given by the following formula:
K~t-:
( 1 + -
) p t ··e
fe (7) Au 1 + (n-l)p
<::>
The column may be designed for an equivalent axial load P8 or Pt .s.s given by the following formula:
p ( K•e )
Pe 1 + C -t--- (8)
The maximum allowable compressive stress in the concrete, fe, in columns subjected to combined axial and bending stre.ss as described above shall not exceed that given by the following formula:
K· e 1 +--
fe ( t K • e )
1 + c
(9)
t
In the case of square or rectangular columns subjected to bending in both planes of symmetry the column shall be designed on the basis of uncracked sections only when the sum of the e/t ratios about both axis does not exceed 0.5. In this case formulas (7), (8) and (9) may be used by substituting for Ke/t the sum of the Ke/t ratios in both planes of bending.
In formulas (7), (8) and (9) for an approximate or trial design K may be taken as 8 for a circular spiral column and as 5 for a rectangular, tied
6-14
or spiral column. The assumed value of K shall be checked for the adopted section.
Reinforced concrete columns, in which the e/t ratio is grea.ter than 0.5 in the case of bending in one plane or in which the sum of the e/ t ratios is greater than 0. 5 in the. case of bending in both planes of symmetry, shall be designed on the bas is of the rEcognized th<::ory for cracked sections, based at: the assumption that no tensim~1
is resi2ted by the concrete.
In such <::.iOlses the modular ratio 0 n, for tr,e compressive reinforcement may ht:: assnmed !iS twice thG value- giv.on in Artie lt; 5. 2 (A); hmvever, the stress in the compresBi'.'e rei.rt:f.or<::ement wheE caleulated on this bs.sis, shall not be greater than the allowabl•.:o stress irt te:r:1sion,
rosr.ncr::r AND fiiRECTION OF NEUTRA.:L X'CIB
A method of determining the locG.tioc. and din::ctiou of the neutral axis is as follows:
Wh<?.n the plar:e of bendir:.g cos,:; not lie ort principal axi"' o:f: thf:' cohm1r1 s;:,ctio<l or whe'.1 the poict: of applic.:ttio:.' of: r.he .resulta:~J.: load does not lis witl,_in t.l:t2 ken:;. area. o:: tht. gros3 trJ.:bformEod ':-'~'ct:i.on~ tJ-,<::, posit ion a:1d direction. of the. nEutral !.ixis r.r.ay b<:-: determined by the followiug formula:
p Mi H'v + Xo±~ Yo 0
A I~ I 'y
I' = load parallel to the axic; oi the columE in pound;:;
A transformed area of crae;ke.d section in squa.re inches
M'x .:. :~\\f:~y.:
M M'y My-Ixy
:; Hx = :0..x
Iy y
IX
(I 2 (Ixy)2 X y)
I' = I I'y = Iy- ~-X X
Iy Ix
~ = Moment of external forces about Y. axis
~ = Moment of external forces about X axis
X Y = coordinate referred to axes passing through the 0 0
centroid of the section.
6-15
Ix moment of inertia about the y axis
T moment of inertia about the X axis -y
T .Lxy= Product of inertia about axis, X and y
In solving the above formula it is necessary to assume a value for either X0 or Y0 •
FORMJJLAS FOR STRES3ES
With the position and direction the neutral axis determined, the:: maximum unit stress in the concrete shall be computed with the formula,
f M' M'x y
Yn or f = xn in which I' y I' X
distance from the neutral axis to the extreme fiber in compression measured parallel to the Y axis,
X n distance from the neutral axis to the extreme fiber
in compression measured parallel to the X axi~.
ThE: limiting steel ratio of 0.04 provided in Article 6.8(D) (1) may be increased to 0.08 for tied columns designed to withstand combint:d axial a:c.d bending stresses provided that the amount of steel spliced by lapping in any 3 foot length of colum...11 shall not exceed a steel ratio of 0.04. The size of the column shall be not less than that required by axial load alone.
6.9~ CONCRETE ARCHES
(A) Shape of Arch Rings
Arch rings shall be selecte.d. as to shap!? in such manner that the axis of the ring shall conform, as nearly as practicable, to either the equilibrium polygon for full dead load or to the equi.librium polygon for full dead plus one=half live load over the full span 1 whichever produces the smallest bending stresses under combined loads.
(B) Spandrel Walls
When the spandrel walls or filled spandrel arches exceed 8 feet in height above the extrados they shall be designed as vertical slabs supported by transverse diaphragm walls or deep counterforts. Vertical cantilever walls over 8 feet in height, or counterforts having a back slope of less than 45 degrees with the vertical, shall not be used, on account of the
6-16
excessive and indeterminate stresses set up in the arch ring by torsion.
(C) Expansion Joints
Ven:ical expansion joints shall be placed in the spandrel walls of arches to provide for movement due to temperature change and arch deflection. These joints shall be placed at the ends of spans and at intermediate points, generally not more than 50 feet apart.
(D} Reinforcement
Arch ribs in reinforced concrete construction shall be reinforced with a complete double line of longitudinal reinforcement consisting of an intradosal system and an extradosal system connected by a series of &tirrupe or tie rods.
For barrel arches, a sys t.e.m of transvers£ reinforcement, thoroughly anchored to tb.e longitudinal reinforcement, shall be used in both intrados and extrados. 'I'he transverse reinforcement sbdll be proportioned to resist the bending stress due to any overtuc1.ing action of the spandrel wall.
For rib arches, hoops or tie bars ahall Le used in connection with the longitudinal rib reinforceme:1c, a;,: in the case of reinforced concrEte columns.
(E) Waterproofing
Preferably, the top of the arch ring and the interior faces of the spandrel walls of all filled spandrel arches shall be waterproofed with a membrane waterproofing.
(F) Drainage of Spandrel Fill
Tl:1e fills of filled apa::1.drd arches shall be effectively drained by a system of th(;' tile drains or Fre.nch drains laid along the intersection of the spar:drel walls and arch rings s.nd discharging through suitable outlets in the piers and abutments, The location and det:ail of the drainage outlets shall be such as to eliminate, as far aq possible. the discoloration by drainage water of the exposed masonary faces.
6.10= VIADUCT BENTS AND TOWERS
VJhen concrete columns are used in viaduct construction, bents and towers shall be effectively braced by means of longitudinal and transverse struts. For height greater than 40 feet, both longitudinal and transverse cross or diagonal bracing, preferably, shall be used, and the footings for the columns, forming a single bent, shall be thoroughly tied together.
6-17
6.11~ BOX GIRDERS
(A) Effective Compression Flange Width
In girder and flange construction, consisting of a girder stem with top and bottom slab, effective and adequate bo:1d and shear resistance shall be provided at the junction of the girder and slab. The slab may then be considered an integral part of the girder, but its effective width as a
girder flange shall not exceed the following:
(1) One fourth of the span length of the girder
(2) The distance centre to centre of girder
(3) Twelve times the least thickrLess of the slab plus the width of the girder stem
For girders having flanges on o:1e side only, the effective overhanging flange width shall not exceed the £allowing:
(1) One. twelfth of the span length of the girder
(2) One-half the clear dis t.ance to the next girder
(3) Six times the least thickness of the slab.
(B) Flange Thickness
(1) Top Flange
lbe mudmum flange thickness shall be 1/16 the clear distance between girders, or 6 inches, whichever is greater.
(2) Bottom Flange
The minimum thickness of the bottom flange shall be determined by maximum allowable unit stresses as specified in (C) and (D) but in no case shall be less than 1/16 of the clear span between girders or 5~ inches, whichever is the greater. Adequate fillets shall be provided at the intersection of all surfaces within the cell of a box girder.
(C) Flexure
(1) Parallel to Girder
The compressive unit stress in extreme fiber of concrete in both girder stem and flange shall not exceed that given in Article 5.2(B)
(2) Normal to Girder
The compressive unit stress in extreme fiber of concrete in the girder flange shall not exceed that given in Article 5.2(B).
(D) Shear
The flange shall not be considered as effective in computing the shear and diagonal tension resistance of girder o,tems 0 except in the determination of the value of j.
TI1e hurizontal shearir1g unit stress at th<? jtmction of the flange and the monolithic fillet joi:ling it to th~ girder stem shall D.ot excesd that given in Article 5.2(B), shear-bt:ams with web reinforcernenL
Changes in girder stem thickness shall be tapered for a minimum distance of 12 times the difference in stem thickness.
(E) Reinforcement
'I11e unit stress in steel for both girder stem and ilange shall ro.ot: exceed that given iTJ. Article 5.3.
(F) Flange Reinforcement
(1) Parallel to Girder
Minimum reinforcement of 0,6 per cent of the flange section, but in no case lesa than requir~d by Article 3.2(E) shall be placed in both top and bottom flangeE, distributed over both surfaces. Where necessa.ry, a single layer of bftrs may be centre.d. in th~;; bottom slab. Bar spacing shall not exceed 18 incht~S.
(2) Normal to Girder
Hinimum reinforcement of 0.5 per cent of the flange section shall be placed in the slab~ di.stri.buted over both f>Urfac.es, Ba:c bpacing shall not exceed 18 in.eh.e;:.;. These bars shall be bent up into the e.xterior· gi.n:l.t:r ,;tem. at le:Lst 10 bar diameters.
Reinforcement in the top flange in a direction transverse to the girders shall extend to the exterior face of all outside girderE', and a minimum of 1/3 of such reinforcement shall either be anchored with 90° bends or ext.t:nded beyond the girder face a sufficient distance to develop the strength of the bar in bond p-rovided the flange projects beyond the girder face a sufficient distance to provide this bond length"
(G) Diaphragms
Diaphragms or spreaders shall be placed between the girders at
6-19
intervals not to exceed 40 feet.
(H) Flanges Supporting Pipes and Conduits
Flanges supporting both vehicle live load and pipes or conduits shall be designed using unit stresses set forth in Article 5.2 and 5.3.
Flanges supporting only dead load of structure and pipes or conduits shall be designed in the direction normal to the girder using unit stresses not exceeding 75 per cent of those set forth in Article 5,2 and 5.3.
(I) Position of Negative Noment Reinforcement.
I;Jhen the floor slab of a box ginier is placed afcer the web walls have taken their set, at least 10 per cent of the negative moment reinforcing steel shall be placi:ed in the web walls. The reinforcing steel shall exten.-1. a distance of one- fourth the spa:1 length each side of the intermediatE: supports of continuous spans, one·~fi:Zth the ,:;pan length from the restrained ends of continuous spans, and the entire length of ca:2ti= lever spans" Ia lieu of the above requi.rf·.'Jlent tv.Jo number 8 bars full length of the webs may be used.
(J) Reinforcement of Web Wall Sides
The web walls between the top and bottom slabs shall have rei~forcing bars placed horizontally in both faces to preve~t temperature and shrinkage cracks. The total area of steel shall not be less than 1/8 sq. in. per foot of height of the unreinforced web walls. The spacing of bars shall not exceed 2 feet.
6-20
Section 7 = PRESTRESSED CONCRETE
7,1= GENERAL
The design of prestressed concrete members of highway bridges shall conform to the requirements of 3ection 6, Concrete Design, insofar as the requirements of that section apply and are not .specifically modified by requirements set forth herein. The specifications of this section are L~lt,;,nderi f•Jc use '.n the ·-~esigr: ot simp lee· span structures of mode:rate length. :.oic~ r gr-: ·.:) l~ ti.:l.t: s 1 ;_cl 1 ::: ~- ~~ ~ -~ ·: =~ 1_; -;-f-; :-; ;_· '-:~·: ~ i-:::- _:~ ,~pee i a 1 c~ t lJd:,: :3.r.l.d d.-::· t a j_ J. ed -·,.:o c: r:-.:.;. i.{-1 E'.r.:::: f~· -L rJr!
Ab bearing area of anchor plate of post-tensioning steel.
Ac maximum area of the portion of the anchorage surface that is geometrically similar to and concentric with the area of the bearing plate of post-tensioning steel.
As = area of main prestressing tensile steel
A's= area of conventional steel.
Asr steel area required to develop the ultimate compressive strength of the web of a flanged section.
A area of web reinforcement. v
b width of flange of a flanged member or width of a rectangular member.
b' width of web of a flanged member.
d distance from extreme compressive fiber to centroid of the prestressing force.
I Moment of inertia about the centroid of the cross section.
I Impact load
j ratio of distance between centroid of compression and centroid of tension to the depth d.
p As /bd, ratio of prestressing steel.
p' A's/bd, ratio of conventional reinforcement.
s longitudinal spacing of web reinforcement.
7-1
t average thickness of the flange of a flanged member,
Q statical moment of cross section area, above or below the level being investigated for shear, about the centroid.
D effect of dead load.
L effect of design live load including impact, where applicable.
Vc shear carried by concrete
Vu shear due to ultimate load and effect of prestressing.
Ec flexural modulus of elasticity of concrete.
Es modulus of elasticity of prestressing steel.
f 1 c compressive cube strength of concrete at 28 days (6 11 cube)
(f'c)= compressive cylinder strength of concrete at 28 days(6n cylinder)
f'ci =
(f'ci)=
f' s
fsu
f' y
n
e
compressive cube strength of concrete at time of initial prestress
compressive cylinder strength of concrete at time of initial prestress.
ultimate strength of prestressing steel.
effective steel prestress after losses
average stress in prestressing steel at ultimate load.
nominal yield point stress of prestressing steel (at 1.0 per cent extension)
yield point stress of conventional reinforcing steel.
base of Naperian logarithms.
K = friction wobble coefficient per foot of prestressing steel.
T0 steel stress at jacking end.
steel stress at any point x, located at a distance x from the jacking end.
~ friction curvature coefficient.
~ total angular change of prestressing steel profile in radians from jacking end to point x.
7-2
1 length of prestressing steel element from jacking end to point x.
7.3~ DESIGN THEORY
The elastic theory shall be used for tht design of prestr~ssed concrere members unde.r design loads at 1;1orking stresses. Tbc members shall be checked by ultimate strength theory for compliance with specified load faclur.
7.4- BASIC ASSUT''l.PTIONS
The following assumptions an,, made for design purposes:
(a) Strains vary linearly over the depth of the YUemGer throughout the entire load range.
(b) { ".) ,,
Before cracking, stress i& linearly proportional to strain. After cracking, tension in the cor!.crete is neglected.
7. 5~ LOA~)ING STAGES
The stat;~ of stress shall be invest:igat:ed under each loading condition that is anticipated in tht' manLlfacttae, handling and service lift:. of l.he structure. The following are some o[ the conditions tbctt may exist:
(A) Initial Prestress
The concrete and steel stresses in the initial stressing of the rnemher before the dead load from other members is effective and hefore loss.c.s due to lengt.h change3 of the concrete aad steel b.ecve taken place. The condition of marJ\tfacture shall be taken into accoun.t, particularly !'lS to whether the dead load of the member itself is pffective.
(B) Transportation and Erection
J?recast members that are to be moved from their place of manufacture shall be designed so that handling is practicable.
(C) Design Load
Stresses in effect after losses and under dead load and the assumed working live load.
(D) Cracking Load
Complete freedom from cracking may or may rwt be necessary at any particular loading stage. Type and function of the structure and type, frequency, and magnitude of live loads should be considered.
(E) Ultimate Load
The ultimate load that a member can withstand without failure shall
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be the sum of the multiples of live and dead loads specified in the formulas given in Article 7.6. The ultimate load capacity shall be that producing moments equal to the ultimate moment of the concrete or steel as given in Article 7.10.
7,.6- LOAD FACTORS
Load factors are multiples of the design load applied to the structure to insure its safety.
The computed ultimate load capacity shall not be less than
1.5 D + 2.5 (L+I)
These load factors are intended for simple spans of moderate length. For long spans, continuous spans and unusual design, special investigation is advisable with probable increase in the ultimate load factors.
7.7- ALLOWABLE STRESS
In general the design of prestressed members shall be based on a maximum concrete cube strength of 6000 psi or a maximum concrete cylinder strength of 5000 psi
(A) Prestressing Steel
(1) Tf}mporary stress before losses due to creepand shrinkage ... 0. 70f's (Overstressing to 0.80 f's for short periods of time may be permitted provided the stress after seating of the anchorage, does not exceed 0.70 f 1 s)
(2) Stress at design load(after losses) 0.60 f' or 0.80 f which ~~ s sy
ever is smaller, or 0. 70 r s less all computed losses.
(B) Concrete
(1) Stress at Transfer before losses due to creep and shrinkage:
Compression Cube strength
Pretensioned members---------- .50 f'ci
Tension
Post.,tensioned members-------- .45 f' ci
Members without nonprestressed reinforcement:
Single element----------------- 2. 75
Segmental element-------------- Zero
7.4
~ ci
Cylinder strength
0.60(f'ci)
0.55(£' .) Cl.
3 VCf' ,) Cl.
Zero
Beams and girders may be comprised of 'single element', or a number of precast elements hereafter referred to as 'segmental elementd.
Hembers with nonprestressed reinforcement sufficient to resist tensile force in the concrete without cracking vJher, computed on H,e basis of au uncracked section:
Single element -----------
~Jegmental element(·,Jithin the element itself)
Cube strength
5 .. '"~ ) fL C i
2.r1 1r~ 1 ' ci
(2) Stress at design load after losses ha·~·e occurred:
Compression-=----------=----- 0.33 f 1
c
Tensio~(in precompressed tensile zone)
?ost-tensioned members Z€·ro
Pretensioned Members 2.75 /f' . , . \ c~ lbut not to exceej 250 ps~;
(3) Cracking Stress
(4)
1:'lexure tensile strength(Hodulus of rupture)from tests or if nor 8Vailable---------------------
Anchorage bearing stress
Post-tensioned anchorage------(_bt!.t not to exceed "'' \ ·· --~ · '·ci "
(A) Friction Losses
~~
6, 8 /f I C -
3
0. 50 .f' cH{A:
~~
Cylinder Strength
3 vc-f· ~) c~
0. 40 { f' ) ., c
Zero
I - . 3 V(f' . ,-,
I! - c~
Friction losset~ in post-tensioned members occur :from angle chat,_ge in draped cables and from wobble of the ducts. These losses can be estimatei
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by the following formula:
(Kl +.P""" ) Tx e
using the follo,;,Jing average values of K and .P
:For small values of K 1 and.,.u~ the following formula can be used.
Type of steel
Wire cables ... , .. , ,
H.igh-strength bars .....
Cal'!anized Strand ..... .
Type of Duct
fright metal sheathing----Galvanized metal sheathing--Greased or asphalt-coated
and wrapped-----------Direct contact with concreteBright metal sheathing-----Galvanized metal sheathing--Direct contact with concreteBright metal sheathing------(~alva:Jized metal sheathing--Direct contact witb. concrete-
K
0.0020 0.0015
0.0020 0.0015 0.0003 0.0002 0.0005 0.0015 0.0010 0.0015
0.30 0.25
0.30 0.45 0.20 0.15 0.40 0.25 0,20 0.50
Friction losses occur prior to anchoring but ,::;hould be estimated. for design and checked during stressing operations.
(B) Prestress Losses
The following sources of loss cf prestress in addition to friction losses, shall be considered to determine the effective prestress.
1. Elastic shortening of concrete
This loss is equal to n (!::!. fc). For pret:e;-1sioned concrete A fc is the concrete stress at the centre of gravity of the prestressing steel for which the lo,:;ses are being computed. For post-tensioned concrete where the steel elements may not be tensioned simultaneously, A fc is the a"verage coucrete stress along one prestressing element from end to end of the beam caused by subsequent post-tensioning of adjacent elements. Taking one half the loss of the first element by subsequent application of prestress from other elements closely approximates the average loss of all elements.
2. Creep of Concrete
Creep is the time-dependent strain of concrete caused by stress. For pre-tensioned and post-tensioned bonded members, concrete stress is taken at the centre of gravity of prestressing steel under effect of prestress and permanent loads ( normal conditions of unloaded structure).
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In post-tensioned unbonded members, stress is the average concrete stress along the profile of centre of gravity of prestressing steel under the effect of prestress and permanent loads. Additional strain due to creep may be assumed to vary from 100 per cent of elastic strain for concrete in very humid atmosphere to 300 per cent of elastic strain in very dry atmosphere.
3. Shrinkage of concrete
The following value of unit strain for shrinkage shall be used:
For pre-tensioned members For post-tensioned members
4. Relaxation of Steel Stress
0.00030 0.00025
Loss of stress due to relaxation of prestressing steel should be provided for in the design in accordance with test data furnished by the steel manufacturer. The loss, generally, is in the range of 2 to 8% of the intial steel stress.
5. Slip at Anchorage
Where a slip of the tendons is expected to take place in seating the anchorage device, the resulting loss of prestress shall be allowed for. An average value of 0.10 inches may be used to compute this loss at each end.
The total prestress losses(except the friction and slip los~may be assumed to be
35000 p. s. i. 25000 p. s. i.
for pretensioned members for post=tensioned members
when data is not available to calculate losses more exactly.
7.9- FLEXURE
Prestressed concrete members may be assumed to act as uncracked members subjected to combined axial and bending stresses within specified design loads. The transformed area of bonded reinforcement may be included in pretensioned members and in post tensioned members after grouting.
7. 10- ULTHiATE FLEXURAL STRENG'l'H
(A) Rectangular Sections
For rectangular or flanged sections in \vhich the neutral axis lies within the flange, the ultimate flexural strength shall be assumed as:
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M u
A s
fsu d (1-0. 7 0 p f su ) f I ~'<
c
(B) Flanged Sections
M u
( 0, 60 p f )
d 1- su (f I C) 'i~·/(
If the neutral axis falls outside the flange, the ultimate flexural strength shall be assumed as:
( 0. 70 Asr fsu)
1- --·----'"-/(
b'd f'c
""k
+ 0, 70 f'c (b-~)t(d-0.5t) +0.85(f'c) (b-b')t(d-0.5t)
Where
A8 r = the steel area required to develop the ultimate compressive strength of the web of a flanged section
A A -A sr s sf
A Steel area required to develop the ultimate compressive sf strength of the overhanging portions of the flange
A = 0. 70 f' (b-~)t /f sf c su
A =0.85 (f' ) (b-b1)t/f sf c su
(C) Steel stress
Unless the value of f can be more accurately known from detailed analysis, su the following value may be used:
Bonded members
Unbounded members
f = f + 15000 su se
Provided that
1) The effective prestress after losses is not less than 0.5 f's 2) The stress relieved wire for prestressing should display a high
yield strength and a reasonable elongation before rupture. Minimum yield strength at 1 per cent elongation under test load should be
'i; 611 compressive cube strength
*'~' 611 compressive cylinder strength
equal to 80 per cent of specified ultimate strength. Minimum elongation after rupture should be 4 per cent in 10 inches.
High strength bars for perstressing should have a m1n1mum yield strength measured by the 0.7 per cent extension under load method equal to 90 per cent of the specified ultimate tensile strength. Hinimum elongation after rupture should be 4 per cent in a length of 20 diameters.
High tensile strength seven \vire strands should conform to the requirements of ASTM designation A416.
7 .11= MAXIMUM AND :t:·flNUHJM STEEL PERCENTAGE
Prestressed concrete members shall be designed so that failure of the steel rather than of the concrete will occur at ultimate load. In general the percentage of steel shall be such that:
For rectangular sections .s.
p " <
fsu I f'c = 0.25 ~ 0.30
For flanged sections
For steel \vith percentage greater than this the ultimate flexural strength shall not be assumed as greater than
For rectangular sections "'< 2
= 0 20 f' bd . c
For flanged sections
M u
0. 20 b 'd2 f' c ....
" I + 0. 70 f' (b-b)t(d-0.5t) c
'id: 2
Mu = 0.25(f'c) bd
2 *"k
M =0.25 b'd (f' ) u c
+0.85(f' )(b-b')t(d-0.5t) c
In prestressed concrete members reinforced with tendons of high tensile strength steel wire or high tensile-strength strand in which t.he anchorage of the tendons is by bond alone, the cross sec.tio::1al area of the tendons shal be not less than 0. 3 per cen-c of the cross sectional areas of the member at the time of the transfer of stress from the prestressing bed to the member.
7.12- NONPRESTRESSED REINFORCEMENT
Nonprestressed reinforcement may be considered as contributing to the
7=9 611 cube strength 611 1 d cy in er strength
tensile strength of the beam at ultimate strength in an amount equal to its area times its yield point, provided that
For rectangular sections
p fsu p' f' y ~ 0.25 +
p fsu p' f' y < + = 0.30 f' •k
f' * c c (f 1 )1c7'> (f I )1d;
c c
For flanged sections
A fsu A' sf' sy sr ~0.25 +
A fsu A' f' sr s s y ~0.30 + b'd f '~'~ b'd £'*
c c b'd (f' )~~* b 'd (f'
... ;... ... t .. ) lb-1\.
c c
7.13- SHEAR
A. The effects of shear may reduce the resistance to cracking ar1d the ultirr.ate strength of flexural members. for uncracked sections, the principal tensile stresses should be calculated at points of maximum shear and at points where there is a significant change of shear or change of section. Shear reinforcement should be provided where necessary in accordance with the provisions of this clause.
B. Where the principal tensile stress d>Je to prestress, bending and shear at working loads exceeds that given in the table below shear reinforcement should be introduced. The proportion of shear to be resiste::l by this reinforcement should be assumed to vary linearly with the principal tensile stress from a value of O,for the stress given in the tableJto 1,0 for a stress of 1.5 times that given. When the principal tensilE: stress is greater than 1. 5 times that given in the Table the whole of the shear should be carried by reinforcement. The area of web reinforcement shall not be less than 0.0025 b's. The spacing of web reinforcement shall not exceed three-fourth the depth of the member or 24 11 , whichever is less, and shall provide transverse reinforcement across the bottom flanges.
C. Shear reinforcement is often desirable for major structural mFOmbers eve:J. when the principal tensile stress is less than the appropriate value in the Table particularly for beams with thin webs, for which recommendations are given in Article 7.19
Specified Strength of Concrete (lbs / sq. in. )
Cube Strength
4500 6000 7500
~~ 6" cube strength
Cylinder Strength
3500 4700 5900
** 6" cylinder strength
7-10
Limiting principal tensile stress for concrete in uncracked sections
at working loads (lbs/ sq. in. )
125 150 175
at ultimate load (lbs/sq. in.
300 350 400
D. Where the principal tensile stress due to shear and effective prestress· at uncracked sections, under the ultimate load, exceeds that given in the Table aboveithe whole of the shear in excess of that resisted by tendons inclined· to the neutral surface should be resisted by shear reinforcement acting at a stress not exceeding 80 per cent of the yield stress( or 0.2 per cent proof stress, where appropriate).
E. Special consideration should be given to the shear resistance under ultimate load conditions where. the section is cracked in bending. The possibility of developing such resistance by means of truss, arch or similar actions should be examined and, where reliaace is placed on one of these, adequate reinforcement, complying with the requirement of the preceding paragraph of this clause, should be provided.
7.14- COMPOSITE STRUCTURES
(A) General
Composite structures in which the deck is assumed to act integrally with the beam shall be interconnected to transfer shear along the contact surfaces and to prevent separation of the elements. Transfer of shear shall be by bond or by shear keys. Tne elements shall be tied together by extension of the web reinforcement or by dowels.
(B) Shear Capacity
The shear connection shall be designed for the ultimate load and may be computed by the formula v V Q/I.
u
(C) Bond Capacity
The following values for ultimate bond resistance at the contact surfaces shall be used in determining the need for shear keys:
When the m~n~mum steel tie requirements of (D) of this article are met--------------------------------------- 75 psi
When the minimum steel tie requirements of (D) of this article are met and the contact surface of the precast element is artificially roughened-------------------=-150 psi
When steel ties in excess of the requirements of (D) of this article are provided and the contact surface of the precast element is artificially roughened--------225 psi
If bond capacity is less than the computed shear, shear keys shall be provided throughout the length of the member. Keys shall be proportioned according to the concrete strength of each component of the composite member.
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(D) Vertical ties
All web reinforcement shall extend into cast-in-place decks. The spacing of vertical ties shall not be greater than four times the minimum thickness of either of the composite elements and in any case not greater than 24 inches. The total area of vertical ties shall not be less than the area of two No.3 bars spaced at 12 inches.
(E) Shrinkage stresses
In structures with a cast-in-place slab on precast beams, the differential shrinkage tends to cause tensile stresses in the slah and in the bottom of: the beams, Stresses due to differential shrinkage are important only insofar as they effect the cracking load. When crackiEg load is significant such stresses should be added to the effect of loads.
7. 15- END ZONE OF CONCRETE I-BEAN[:l
For beams wit:h post-tensioning ten.Jons, end blocks sh.all be used to di.strihute thP coneentratec prestress:Lrrg forces at the anchorage. Where all tendons are pre tensioned ·wires or 7-wirt;, .strand, the use of end bloeks will not be required.
End blocks shall have sufficieni: area to allow the sps.cing of the prestressing steel as speci~ied in article 7.16 . Preferably, they shall be as wide ar-: the narrower flange of the beam, Th,:;y shall have a le:Jgth at least equal to three fourth of th2 depth of the beam and in any case 24 inches. In post ten,:;ioned members a closely spaced grid of bo•:h vertical and horizontal bars shall be placed near the face of the end block to resist bursting and closely spaced rein£orceme.nt shall be placed both vertically and horizontally throughout the length of the block.
In pretensioned beams, vertical stirrups acting at a unit stress of 18000 p.s.i. to resist at least 4 per cent of the total prestressing force shall be placed within the distance of d/4 of the end of the beam, the end stirrup to be as close to the end of the beam as practicable.
7. 16- COVER AND SPACDlG OF PRESTRESSING STEEL
(A) Minimum Cover
The following m:Lnlmum concrete cover shall be provided for prestressing and conventional steel:
Prestressing Steel and Main reinforcement 1~ inches Slab reinforcement: bottom of slab 1 inch, top of slab 1~ inches >'ci:
Stirrup and ties 1 inch **May be reduced to one inch where an additional wearing surface is to be used.
7-12
In location where members are exposed to salt water, salt spray or chemical vapor, additional cover should be provided.
(B) Minimum Spacing
The mlnlmum clear spacing of prestressing steel at the ends of beams shall be as follows:
Pretensioning Steel: Three times the diameter of the steel or 4/3 the maximum size of the concrete aggregate, whichever is grea':er.
Post- tensioning duets: 1-Iorizontally = l}z inches or l}z times the maximum size of the aggrP.gate, whichever is the greater. However,there should be sufficient gaps between the tendons to allow the largest size of aggregate used to move, under vibration, to all parts of the forms. At the ends the spacing will be governed by the end details of the type of the system used. The inside diameter of post tensioning ducts shall be at least one fourth inch greater than the diameter of the prestressing steel.
(C) Bundling
When prestressing steel is draped or deflected, not to exceed three ducts may be bundled in the middle third of the beam length provided that the spacing specified in (B) is maintained in the end three feet of the member.
7.17- EMBEDMENT OF PRESTRESSING STRAND
To insure proper bond in pretensioned members designed to resist flexure, the following minimum length of embedment of seven-wire strand, measured from the free end of the strand to the point of maximum steel stress at ultimate flexural strength, shall be as follows:
1/2 inch strand 7/16 inch strand 3/8 inch strand 1/4 inch strand
7.18- CONCRETE STRENGTH AT STRESS TRANSFER
135 120 100
65
inches inches inches inches
Unless otherwise specified, stress shall not be transferred to the concrete until the compressive strength of the concrete, as indicated by test cubes or cylinders cured by methods identical with the curing of the members, is at least 80% of the 28 day compres~ive strength.
7 . 19- REINFORCEMENT IN BEAMS
Reinforcement may, in cert3in circumstances, be desirable in prestressed concrete beams.
It should be noted that steel reinforcement lying parallel to the
7-13
axis of prestress in a prestressed concrete member may at some time act as longitudinal reinforcement in compression. Transverse binding may be required to prevent buckling of this reinforcement particularly if its diameter is large.
Reinforcement will often be required at the ends of members to take the tensile stresses that may be induced near the ends by the prestressing force and particularly stresses caused during transfer.
Reinforcement may be necessary, particularly where post~tensioning systems are used, to control any cracking resulting from restraint to longitudinal shrinkage of members provided by the formwork during the time before the prestress is applied.
Web reinforcement is desirable in beams with thin we~s, particularly whe:1 ducts or tendons are located in the webs. Generally in beams of depth exceeding 2 ft. and length exceeding 30 ft. in which the depth of the web is more than four times the web thickness, vertical reinforcement is desirable in the form of stirrups. \-Jhere this reinforcement is provided in the form of mild steel bars its total croSS"'Sectior• area should be not less than 0.1 per cent of the sectional a.rea in plan of the web. Where high tensile steel is used, the area of this reinforcement may be reduced with respect to the area of mild steel otherwise required, ic the inverse ratio of the corresponding permissible stresses. In either case, this reinforcement should preferably not be spaced further apart than a distance equal to the clear web depth. The size of such reinforcement should be as small as practicable.
Where prestressed concrete beams may be required to resist shock loading, the beams should be reinforced with closed stirrups and longitudinal reinforcement of mild steel.
7-14
SECTION 8 - PILE LOADS AND BEARING POWER OF SOILS
8. 1- BEARING POWER OF FO!JNDATION SOILS
When required by the engineer, the bearing power of the soil in excavated foundation pits shall be determined by loading tests. The following tabulation of the bearing power of broad basic groups of materials may be used as an aid to the judgement in the absence of more definite information:
Material
Alluvial soils ---------------Clays ---~-----------Sand, confined ---=-"--------Gravel -~------------= Cemented sand & gravel --------Rock ---------------
Safe bearing power Tons per square foot
Min, Max.
!z 1 1 4 1 4 2 4 5 10 5
Loading tests have a limited depth influence and may not disclose long-time consolidation.
When the consolidation of foundation soils causes the settlement of the backfill against an abutment or the settlement of the soil under an ahutment: which is placed on piles dri'l;'en through a fill, the load transmitted may result in overloading the piles.
When the hydraulic gradient is increased as in excavating material from below the water table, foundation soils may be loosened by the upward flow of water. Such a condition should be guarded against.
Intrusion failures should be prevented by requiring a base course between rip rap and fine soils and by requiring proper gradation of drainage backfill behind abutments.
8.2~ ANGLES OF REPOSE
Earth, Loam ----=30°to 45° Gravel 30° to 4D0
Dry Sand -----25 to 35 Cinders 25 to 40 Moist Sand ____ ;,.30 to 45 Coke 30 to 45 Wet Sand =----15 to 30 Coal 25 to 35 Compact earth ----35 to 40
In the absence of exact data which has been determined by field investigation and soil analysis, the angle of repose of the material shall be assumed to be the minimum given in the table.
8-1
8.3- BEARING VALUE OF PILING
(A) General
The design loads for piles shall not be greater than the minimum value which shall be determined for Case A, Case B, and Case C; where Case A is the capacity of the pile as a structural member, Case B is the capacity of the pile to transfer its load to the ground and Case Cis the capacity of the ground to support the load delivered to it by the pile or piles. The values assignable to each of the three cases shall be detErmined by making subsurface investigations or tests of sufficient extent to justify the assumed design values used for the particular condition of support under consideration.
In determining the bearing value of piles for use in designiag, consideration shall be given to all information available relative to the sub-surface conditions. Consideration shall also be given to:
(l) The difterence be tween the supporting capacity of: "'· sieic!;le pile and group.
(2) The capacity of the underlying stra.ts. to support the load of the pile group.
(3) The effect of driving ad~ i.tional piles aod the effect or: their loads on adjacent structureso
(4) Possibility of scour and its effect
(J3) Cc.se .!J, .• Capacity of Pile as a. ~itructural Member
(1) Structural Columns:
Piles shall be designed a;;; structural columns 0 Concret:e piles shall be designed in accordance with Article 5.2 1 steel pile& in accordance with Article 504, and cor..crete-filled pipe piles in accordance with Article 5. 2, except that the allowable unit stresPes may be increased 20% provided the shell thickness iA not less tha!t ~ inch. The are&. of the shell shall be included i'1 determining the value p, (percentage of reinforcement), Where corrosion may be expected l/16 inch shall be deducted from the shell thickness to allow for reduction in section by corrosion, The allowable stresses of Article 5.4 and 5.2 may be used in all cases where all of the stresses to which the piles may be subjected have been included. These stresse,::; may be increased in accordance with Article 5 .1. For trestle piles or other piles without lateral support designed for dead load and live load only and where temperature, traction, water pressure and other forces are not considered, the allowable unit stresses specified in Article 5.2 and 5.4 shall be decreased 20%.
8-2
Sub~-;urL;.ct: invest.igat.ions :,hall bE' 'nade which >vll1 de.t:er>.T•it:<" the proba.hle depth of H.ou.,r- or flotB.tiO'' of mat.:eria.l d'1d tie corcditim; of lateral ~upport of lhe pile.
(C) Ca;>e :!). Capaciry of Pilt:> 1·o 'Transfer lo;-;d to che GroilLd:
(1) Point-bearing Piles
A pile shall he co01sidered to be a point=b-e.3.r iug pile whei< placed or driven on or into a material \.fhich is capa!::Jle of developing the pile load by direct bearing at the point with reasonable factor of safetyo
The allowable load at t:ip of the pile shall not exceed i.·h.e
following:
(a) For concrete piles. 0.26 f'c *or 0.33(f'c)**
(b) :!Tor concrete= filled pipe piles . 32 f; c·k or . 40 (f' c)-?e* in accordance with Article 5.2~ applied to the total actual area of the concrete and steel.
(c) For steel piles 9000 pounds per sq. in. over the cross sectional area of the pile tip.
The limitation in (b) and (c) govern except where the poh1t bearing capacity of the piles is determined by loading test piles.
(2) friction Piles: A pile shall be considered to be a friction pile if its point
does nol re.st on or in a material '1.vhicb is capable of de-~7eloping the pile load by direct bearing at the point,
The load-carrying capacity o:f friction piles shall be determined by one or more of the following methods:
(a); Driving and loading test piles.
(b) Pile=driving experie::1ce in the vicinity, When pile.s are designed on the basis of experience in the ~icinity, du(:' consideratimt will he given to the variation in pile types and lengths, and in the variation of the soil strata. Where possible the complete drtving records of <ill piles in the vicinity shall be exami:1ed and comparEd to the driving recordd of the project piles.
(c) Adequate tests of the soil Btrata t:hrough which the pile is to be driven. These tests should be projected a:o.d compared, if posaible, to tests of similar material through which piles of known capacity have been driven,
8-3
6 11 compressive cube strength
6 1' compressive cylinder strength
(3) Required Subsurface Investigations
(a) Point=bearing piles. Sufficient borings shall be m3de to determine the presence, position, and thickness of the material which is capable of developL:g poi:1t=bearing, and the log of borings shall show the nature of the overlying strata in order that the extent of lateral support may be determined. If the point< bearing str3 tum is of doubtful thickness and quality, the borings shall be made to such sufficient depth belm,; this stratum tha.t the cBpacity of a friction pile may be determined.
(b) Fricticn piles. Borings shall be made to an elevatio~l well helow the expected elevation of the pile tips ai'.d accu.rate logs of the::;e borings shall be made. I::;. ttose casE:s where t1~ piles are to be designed on the basis of soil tests, undistrubed samples shall be taker.. on all strata which will have appreciable influer,ce on the capacity of the pile.
(c) Combination point-bearing and friction piles. Piles shall be classified as either (1) point=bearing or (2) friction, ThosP cases where adequate strength is developed by both point bearing and friction may be designed under either of these classifications.
(D) Case C. Capacity of the Ground to Support the Pile L,Jad
Preference shall be given to the determination of. maximum loads on piles by test loading or by satisfactory subsurface investigation.
The capacity of the ground to support the load delivered by the pile shall be determined from the results of the applicable subsurface investigations:
(1) Point-bearing Piles
Sufficient borings shall be made to determine the thickness and quality of the stratum {n which the point bearing is developed, If that stratum is of sufficient thickness and is underlain by a firm material, no reduction will be made for group action of piles. In general, piles should not rest on a thin stratum of hard material which is underlain by a thick stratum of soft or yielding material, but ivhere this condition cannot be avoided, group action should be considered and the design loads reduced accordingly.
(2) Friction Piles
Borings shall be carried well below the tips of the piles in order to determine the characteristics of the underlying material. In most cases a study of those borings will suffice to determine whether or not the underlying soil will support the loads delivered to it, but
8-4
in doubtful or special cases, especially large foundation areas and important footings the material should be in-,restigsted more thoroughly by soil mechanics methods.
A single row of piles shall not be considered as group provided that they are not spaced closer ce::.1tre to centre than 2.~ times the nominal diametsr or dimEmsiorL 1':": th.o3E: cae<:;s '"'here piles are drive':. iE group.t; into plastic materi~l the. d0sig::1 load. shall !:le determi~tsd
by th8 loading of a group of piles or definite gllowauce shall be made for i:he difference het:wee·::-. the suppo.rt:ing capaci-c:;· of &. r:ingle pile and a group of pile:;. Refer to (G)
(E) Maximum Design Loads for Piles
In those cases where it i.s not feasihle to make the required sucdnr:Eace iav~Cstig'ltions or test load.s the maximum assumed desigE load for piles shall be as given in the table b•dow, Tl:ese yalut:i3 may be L:lC:rt:oa<:'ed f0r certain combinations of loadtl as spPcified i:1 ~".rticle 5, 1,
Size or Diameter in inches
8 10 12 14 16 20 24
(F) liplift
'l'YPFS or P:I:LI::S
Concrete Tons
20 24 28 32 40 50
Steel (·-~ , , )T tr~Ctl.OD. · 0:15
16 20 24 28
Steel l'oin.t Bearing
9000 pounds per sq. in, of point area
Friction piles may be considered to resist aa intermittent but not suetained uplift equivalent to 40 per cer.t of the above loads pro7iding proper provision i.::. made for th.e. s:c:;.chor.age at top and sufficie:.lt skin fr:icti.oD is dev£;loped a!ld in r,.o case Bhall it exceed the weight of mat<.:rial (buoy&.:ncy considered) surrom1.di':tg ttt embeded portion of the pile,
(G) G:coup Pils Loading
Where the capacity of a gro:c.p o:f frictio:::J. piles driver: iro.to plastic material is not determined by test loading, the following Co::lverse~LabEtrre
formula is suggested to determim: the reduc tio·c. oi a singlE, pile load for a group pile load:
(n = 1) m + ( m - l) n E = 1 - ~
90 1Jl TI
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Where
E the efficiency or the decimal fraction of the single pile value to be used for each pile i~ the group"
n = the number of piles in each row
m the number of rows in each group
d the average diameter of the pile
s = centre to centre spacing of piles
Tan ~ = d/s
~ is numerically equal to the angle expressed in degrees.
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SECTION 9 - SUBSTRUCTURES AND RETAINING \..JALLS
9" 1.. PILES
(A) General
In general, piling shall be used when footings cannot, at a reasonable expense, be founded on rock or other s0lid foundation material. At locaticms where unusual erosion may occur and the soil conditions permit the driving of piles, they, preferably)shall be used as a protection against scour, even though the safe bearing resistance of the natural soil is sufficient to support the structure without piling.
In general, the penetration for any pile shall be not less than 10 feet in hard material and not less than 1/3 the length of the pile nor l2.ss than 20 feet in soft material ..
For foundation work, no piling shall be used to penetrate a very soft upper stratum overlying a hard stratum unless the piles penetrate the hard material a sufficient distance to rigidly fix the ends.
(B) Design Loads
The design loads for piles shall be according to Article 8,.3,
Piles shall be desLgned to carry the entire superimposed load, no allowance being made for the supr;orti.ng value of the material between the pile 3,
The supporting power of piles shall be determined by the application of test loads.
(C) Spacing, Clearances and Embedment
Footing areas shall be so proportioned that pile spacing shall be not less than 2 feet 6 inches centre to centre, \<Jhen the tops of foundation piles are incorporated in a concrete footing, the distance from the side of any pile to the nearest edge of footing 3hall not be less than 9 inches.
The top of steel piles shall project not less than 12 inches into the concrete after all damaged material has been removed. The penetration of concrete piles shall be not less than 6 inches.
(D) Batter Piles
When the lateral resistance to the soil surroundiP.g the piles is inadequate to counteract the horizontal forces transmitted to the foundation or t-1hen increased rigidity of the entire structure is required, batter piles shall be used in the foundation.
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(E) Buoyancy
The effect of hydrostatic p=essure shall be considered in the design as provided in Article 2. 15.
(F) CDncrete Piles (Precast)
Precast concrete piles shall be of approved size and shape. If a square section is employed, the corners shall be chamfered at least one inch,, P:Ues, preferably, shall be cast with a driving point and for hard driving, preferabl:J shall be shod with a metal shoe of approved pattern" Piliug :nay be either of uniform section or tapered" In ge:::~eral, tapered piling shall not be used for trestle construction except for that portion of the pile which lies below the ground line; nor shall tapered piles be used in any location where the piles are to act as columns c. In general, concrete piles shall have a cross sectional area, measured above the taper, of not less than 140 square inches and when they are to be used in salt water they shall have a cross sectional area of not less than 220 square inches ..
The diameter of tapered piles measured 2 feet from the point shall be not less than 8 inches, In all cases the diameter shall be considered as tr:e least dimension through the centre. The point in all cases, where steel points are not used, shall be not less than 6 inches in diameter and the pile shall be beveled, tapered or sloped uniformly from the point to 2 feet from the point.
Vertical reinforcement shall be provided consisting of not less than four bars spaced uniformly around the perimeter of the pile. It shall be at least l];z per cent of the total cross scctio!1 measured above the tapper, except that if more than four bars are used, the number may be reduced to four in the bottom 4 feet of the pile.
The full length of vertical steel shall be enclosed with spiral reinforcement or equivalent hoops.
The spiral reinforcement at the ends of the pile shall have a pitch of 3 inches, and gauge of not less than NooS(Eirmingham). In addition the top 6 inches of pile shall have five turns of spiral winding at one-inch pitch.
For the re;:nainder of the pile the vertical steel shall be enclosed with spiral reinforcement No.5 gauge(Birmingham), with not more than 6-i.nch pitch, or with l:Lnch round hoops spaced not more than 6 inches on centres.
4 The reinforcement shall be placed at a clear distance fror.J. the face of
the pile of not less than 2 inches and when the piles ar2 for use in salt water or alkali soils this clear distance shall be not less than 3 inches.
In computing stresses due to handling, the computed static loads shall be increased by 50 per cent as an allowance for impact and shock.
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(G) Concrete Piles (Cast-in-Place)
Cast-in-Place concrete piles shall be , in general, cast in metal shells which shall remain permanently in place. However, other types of cast· in-place concrete piles, plain or reinforced, cased or uoc-ased, may be used if, in the opinion of the engineer, the soil conditions permit their use and if their design and the method of placing are satisfactory to him.
Cast-in-place concrete piles may be of either uniform section or tapered or a combination thereof. The minimum size, measured at the butt, or above the taper, and embedment of reinforcement shall be as specified for precast piles, except that foundation piles may have a minimum butt cross-section area of 100 square inches. The minim~~m diameter at tip of pile shall be 8 inches.
Cast-- in~plae:e piling shall be reinforced when specified or shown on the plans. Cast~ in-place foundation piling, carrying axial loads only and where the possibility of lateral forces being applied to the piles is ircsignificant, need not be reinforced ~1en the soil provides adequate lateral support. Those portions of cast· in·place piling which are not supported laterally shall be designed as reinforced concrete columns in accordance with Article 6.8, and the reinforcing steel shall extend ten feet below the plane ~vhere the soil prov~des adequate lateral restraint. Where the shell is more than 0.12 inch in thickness, it may be considered as reinforcement.
Sufficient reinforcement shall be provided at the junction of the pile with the superstructure to make a suitable connection.
The metal shall be of sufficient thickness and strength so that the shell will hold its original form and show no harmful distortion after it and adjacent shells have been driven and the driving core, if any, has been withdrawn. The design of the shell shall be approved by the engineer before any driving is done.
(H) Steel Piles
(1) Thickness of Metal
Steel piles shall have a m~n~mum thickness of web of .40011
Splice plates shall be not less than 3/8 inch thick.
(2) Splices
Piles shall be spliced to develop the net section of pile. The flanges and web shall be either spliced by butt welding or with plates, welded, riveted or bolted. The bolted splices shall only be used on projects where a small number of piling are required and where facilities for riveting or welding are not available.
Splices shall be detailed on the contract plans.
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(3) Caps
In general, caps are not required for steel piles embedded in concrete. Reference is made to Research Report No.1, "Investigation of the Strength of the Connection between a Concrete Cap and the Embedded end of the Steel .H-Pilelf - Department of Highways, State of Ohio, U ,, S ,A, for a discussion of this subject and for the results of the tests pertinent to it.
(4) Scour
If heavy scour is anticipated, consideration shall be given to design of the portion of the pile which would be exposed, as a column.
(5) Lugs, Scabs and Core-stoppers
These devices may be used to increase the bearing power of the pile where necessary. They may consist of structural shapes, welded, riveted or bolted, of plates welded between the flanges, or of concrete blocks securely fastened.
(I) Steel Pile and Steel Pile Shell Protection
Where conditions of exposure warrant, concrete encasement shall be used on steel piles and steel shells or 1/16 inch depth of thickness shall be deducted from all exposed surfaces in computing the area of steel in the piles or shells.
9.2- FOOTINGS
(A) Depth
The depth of footings ahall be determined with respect to the character of the foundation materials and the possibility of undermining. Except where solid rock is encountered or in other special cases the footings of all structures other than culverts, which are exposed to the erosive action of stream currents, preferably, shall be founded at a depth of not less than 4 feet below the permanent bed of the stream. Stream piers and arch abutments, preferably, shall be founded at a depth of not less than 6 feet below strean1 bed. Yne above preferred minimum depths shall be increased as conditions may require.
Footings not exposed to the action of stream currents shall be founded on a firm foundation and below frost.
Footings for culverts shall be carried to an elevation sufficient to secure a firm foundation, or a heavy reinforced floor shall be used to distribute the pressure over the entire horizontal area of the structure. In any location liable to erosion, aprons or cut-off walls shall be used at both ends
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of the culvert and, where necessary, the entire floor area between the wing walls shall be paved. Baffle walls or struts across the unpaved bottom of a culvert barrel shall not be used where the stream bed is subject to erosion. When conditions require, culvert footings shall be reinforced longitudinally.
(B) Anchorage
Footing on inclined smooth solid surfaces which are not restrained by an overburden of resistant material, shall be effectively anchored by means of anchor bolts, dowels, keys or other suitable means.
(C) Distribution of Pressure
All footings shall be designed to keep the maximum soil pressures within safe bearing values. L1. order to prevent unequal settlement, footings shall be designed to keep the pressure as nearly uniform as practicable. In footings having unequal pressures and requiring piling, the spacing of the [Jiles shall be such as to secure as nearly equal loads on each pile as may be practicable.
(D) Spread Footings.
Spread footings which act as cantilevers may be decreased in thickness from the junction of the footing slab with column or wall toward the edge of the footing, provided sufficient section is maintained at all points to provide the necessary resistance to diagonal tension and bending stresses. This decrease in section may be accomplished by sloping the upper surface of the footing or by means of vertical steps. Stepped footings shall be cast monolithically.
(E) Internal Stresses in Spread Footings
Spread footings shall be considered as under the action of downward forces, due to the superimposed loads, resisted by an upward pressure exerted by the foundation materials and distributed over the area of the footings as determined by the eccentricity of the resultant of the downward forces. Where piles are used under footings, the upward reaction of the foundation shall be considered as a series of concentrated loads applied at the pile centres, each pile being assumed to carry its computed proportion of the total footing load.
When a single spread footing supports a column, pier or wall, this footing shall be assumed to act as a cantilever. When two or more piers or columns are placed upon a common footing, the footing slab shall be designed for the actual conditions of continuity and restraint.
Footings shall be designed for the bending stress, diagonal tension stress and bond at the critical section designated herein.
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The critical section for bending shall be taken at the face of the column, pedestal or wall. In the case of columns other than square or rectangular, the critical section shall be taken at the side of the concentric square of equivalent area. For footings under masonary walls, where bond between the wall and footing is reduced to friction value, the critical section shall be taken as midway between the middle and the face of the wall. For footings under metallic column bases, the critical section shall he taken as midway between the face of the column and the edge of the metallic base. The load shall be considered as ueiformly distributed over the column, pedestal or wall, or metallic column base.
The critical section fer bond shall be taken at the same plar..e as for bending, and the shear used for computing bond shall be based 0:1 the same loading and section as for bending. Dor-:d should also be im~estigated at planes where changes of section or of reinforcemen~ occur.
The critical section for diagonal tensio:1. in ::':ootings on soil or rock shall be considered as a conce:1tric vertical section through the footing at a dif'tance "d" from each iace of the colurrm, pedestal, or wall; 11d 11 being equal to the depth fror,1 the top of the section to the centroid of the longitudir:.al tensiol! reinforcement.
The critical section for diagonal ter.:sion in footings supported on piles shall be considered as the concentric vertical section through the footing at a di:~tance, d/2, from each face of the colur.m, pedestal or wall, and any piles whose centres are at or outside this sectioD shall be cotLsidered in computing the diagonal tension.
In sloped or stepped footings, stresses should be investigated at sections where the depth changes outisde the critical section as defined at)ove.
Bending need not be considered ualess the projection of the footing is more than two-third of the depth.
In plain concrete footings, the stresses shall be computed on the basis of a monolithic section having a depth measured from the top of the footing to a phme 2 inches above the bottom of the footing. The maximum fibre stress due to bending shall not exceed that specified in Article 5.2 and the average shearing stress 0!.1 the concentric vertical section through the footir1g at. a distance (d minua 2 i::1ches) from each face of the colurm:1, pedeatal or wall, shall not exceed the shearing stress specified in Article 5.2 for beam without web reinforcement and with longitudinal tars not anchored.
(~) Reinforcement
Footing slabs shall be reinforced for ber..ding stresses and, where necessary, for diagonal tension. The computed stress in the bar shall be developed in bond.
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The reinforcement for square footings shall consist of two or more bands of bars. The reinforcement necessary to resist the bending moment in each direction in the footing shall be determined as for a reinforced concrete beam; the effective depth of the footing shall be the depth from the top to the plane of the reinforcement. The required reinforcement shall be spaced uniformly across the footing, unless the footing width is greater than the side of the column or pedestal plus twice the effective depth of the footing, in which case the width over which the reinforcement is spread may equal the width of the column or pedestal plus twice the effective depth of the footing plus one-half the remaining width of the footing. In order that no considerable area of the footing shall remain unreinforced,additional bars shall be placed outside of the width specified,but such bars shall not be considered a,: effective in resisting the calculated bending moment. For the extra bars a sp~·
cing double that used for the reinforcement within the effective belt may be used.
(G) Transfer of Stress from Vertical Reinforcement
The stresses in the vertical reinforcement of columns or walls shall be transferred to the footings by extending the reinforcement into them a sufficient distance to develop the strer..gth of the bars in bond,or by means of dowels anchored in the footings and overlapping or fastened to the vertical bars in such manner as to develop their strength. If the dimensions of the footings are not sufficient to permit the use of straight bars, the bars may be hooked or otherwise mechanically anchored in the footings.
9. 3- ABUTMENTS
(A) General
Abutments sb.all be designed to withstand earth pressure as specified l.n Article 2.16, the weight of abutment and superstructure, live load over any portion of the superstructure or approachj fill, wind forcee,longitudinsl force when the bearings. are fixed, and longitudinal forces due to frictional bearings. The design shall be investigated for any combinatio:il of these forces which may produce the most severe condition of loading.
Abutments shall be designed to be safe agah~st overturning about the toe of the footing, against sliding or. the footing base and against crushing of foundation material or overloading of piles at the point of maximum pres
In computing stresses in abutments, the weight of filling material directly ovc=r an inclined or stepped rear face, or over a reinforced concrete spread footing extending back from the face wall, may be considered as part of the effective weight of the abutment. In the case of a spread footing, the rear projection shall be designed as a cantilever supported at the abutment stem and loaded with the full weight of the superimposed material,unless a more exact method is used.
The cross section of stone masonry or plain concrete abutrnents shall be proportioned to avoid the introduction of tensile stress in the material.
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(B) Reinforcement for Temperature
Except in gravity abutments, not less than 1/8 square inch of horizontal reinforcement per foot of height shall be provided near exposed surfaces not otherwise reinforced, to resist the formation of temperature and shri~kage cracks.
(C) Wing Walls
Wing walls shall be of sufficient le:1gth to retain the roadway err,bankment to the required extent and to furcish protection against erosion. For ordinary materials, in the absence of accurate data, the slope of the fill shall be assumed as 1~ horizontal to one vertical and wing lengths computed on this basis.
1-Jbere deflec~ion joints are not used reinforcement rods or other suit·~
able rolled sectioEs preferably shall be spaced across the junction betweerl all wing walls a~d aht1tments to thoroughly tie them together. Such bars shall extend into the masoary o:1 each side of the joint :far enough to develop the strength of the bar as Gpecified for bar reinforcement, &:r:d shall vary ir. le:lgtt, so as to hVoid planes of weakness in the cor,crete at their ends. If bars are not used, an expansion joint shall be provided at this point in which the wings shall be mortised into the body of the abutment.
(D) Drainage
The filling material behind abutment shall be effectively drained by weep holes witt French drains, placed at suitable intervals.
9. 4~ RETAINING \..JALLS
(A) General
Retaining v:alls shall be designed to withsta:-;d eacth pressure, includ· ing any live load s·1reharge, and the weight of the wall, in accorda:1ce with the general principles specified above for abutments.
Stone masonry and plain concrete walls shall be of the gravity type. Reinforced concrete walls may be of either the cantilever. counterforted, buttressed, or cellular types.
(E) Base or Footing Slabs
The rear projection or heel of base slabs shall be designed to sepport the entire weight of the superimposed materials, unless a more exact method is used.
The b~se slabs of cantilever walls shall be designed as cantilevers supported by the walls.
9-8
The base slabs of counterforted and buttressed walls shall be designed as fixed or continuous beams of spans equal to the distance between cou~ter= forts or buttresses.
(C) Vertical Walls
The vertical stems of cantilever walls shall be designed as cantilever supported at the base.
The vertical or face walls of counterforted and buttressed walls shall be designed as fixed or continuous beams. The face walls shall be securely anchored to the supporting comiter forts or buttressed by means of adequate reinforcement.
(D) Counterforts and Buttresses
Counterforts shall be designed as T-beams. Buttresses shall be desig~ ~·ed as recta:.1gular beams. In con:r1ection with the mai:l tension reinforcement of counterforts there shall be a system of horizontal and vertical bars or stirrups to eff(O,ctL•ely a.:1chor the face \valls and base slabs, 'I'hese stirrups shall he anchored as near the outside faces of the face walls, and as near ~o
the bottom of the base slab as practicable.
(E) Reinforcement for Temperature
r~xcept in gravity walls not less than 1/8 square inch of horizontal reinforcement per foot of height shall be provided near exposed surfaces not otherwise reinforced, to resist the formation of temperature and shrinkage cracks.
(F) Expansion and Contractio~ Joints
Contraction joints shall be provided at intervals not exceeding 30 feet and expansion joints at intervals not exceeding 90 feet, for gravity or reinforced concrete walls.
(G) Drainage
The filling material behind all retaining walls shall be effectively drained by weep holes with French drains, placed at suitable intervals. In counterforted walls there shall be at least one drain for each pocket formed by the counterforts.
9. 5- PIERS.
Piers shall be designed to withstand dead and live loads superimposed thereon; \.vind pressures acting on the pier and superstructure; the force due to stream flow, centrifugal force, earthquakes, floating drift; and longitud~ inal forces at the fixed end of spans.
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SECTION 10 - STEEL DESIGN
10.1-DESIGN AND CONSTRUCTION
The design of steel bridges shall conform to the British Design Standard 153, Part 4. Design and Construction of the British Standards Institution 1958 Edition.
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