design guide joist girder rev4 final 11sep06

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STEEL JOIST INSTITUTE

Engineering Design Guide Procedure For Joist Girders

Approved by the Board of Directors November 7, 1983

Revision 0

Revision 1 Approved by the Board of Directors 02-01-1993

Page 23 Added Top Chord Fillers-Design Check for Required Weld Length

Revision 2 Approved by the Board of Directors 09-09-1993 Page 8(A) Added Shear Capacity Check of Chord Members (Page originally dated 06-17-1992 and revised 09-23-1992; also shows Issued 04-01-1993)

Revision 3 Approved by the Board of Directors 09-01-2000 Page 8(B) Added Bearing Capacity Check of the Outstanding Leg of the Compression Chord of the Joist Girder under the Reaction of the Joist Bearing on it (Page originally dated 02-01-2000)

Revision 4 Approved by the Board of Directors 11-07-2006 Complete document revised to be in accordance with the 2005 Standard Specifications for Joist Girders (ANSI SJI JG-1.1)

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Table of Contents

Section Description Page 1 GENERAL INFORMATION 4 2 GLOSSARY OF TERMS 6 3 EXAMPLES OF JOIST GIRDER DESIGN CHECKS 10 3.1 EXAMPLE 1A 10 3.2 EXAMPLE 1B 32 3.3 REFERENCES 57 4 PRESENTATION OF ENGINEERING DATA 58

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STEEL JOIST INSTITUTE

ENGINEERING DESIGN GUIDE AND STANDARD DESIGN FORMAT FOR JOIST GIRDERS

As approved by the Board of Directors of the Steel Joist Institute on November 7, 2006 The following comments and sample calculations are offered to:

1) Aid the satisfactory presentation of design data; and 2) Assist in the efficient review of these data by the Consulting Engineer of the

Steel Joist Institute.

A member company of the Steel Joist Institute is responsible for updating its design program and/or design in accordance with specification changes. The revised design must be approved within eighteen months of written notification from the Managing Director of the required change, or as otherwise specified by the Board of Directors.

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SECTION 1 GENERAL INFORMATION

A. Accuracy – Mathematical correctness is necessary; a stress ratio not exceeding 1.01 is acceptable.

B. Effective Depth – No variation from the nominal depth is permissible in design

calculations. The effective depth shall be the distance between the centers of gravity of the top and bottom chords.

C. Cold-Formed Members

The equations presented in the joist girder design examples are applicable to hot rolled members and are based on the 2005 AISC Specification for Structural Steel Buildings. When cold-formed members are used for chords and webs the following requirements apply.

1) Cold-Formed Angle Chords:

a. Q shall be calculated based on the following equation1:

2

0.6

w 63.30.6 for t

63.3 1440.767 0.00264 for

8000 144 for 25

c

y

c yy

c y yy y

cy

FQF

where

F FF

w wF F Ft F t F

wFF tw

t

=

= ≤

⎛ ⎞= − < <⎜ ⎟⎝ ⎠

= ≤ ≤⎛ ⎞⎜ ⎟⎝ ⎠

b. Use 2005 AISC Specification Equations to determine the chord available strength.

c. Use a resistance factor, φ, of 0.9 and a safety factor, Ω, of 1.67.

2) Other Cold-Formed Chord Shapes:

a. Use the 2001 AISI Standard North American Specification for the Design of Cold-Formed Steel Structural Members with 2004 Supplement for the calculation of nominal strength.

b. Use a resistance factor, φ, of 0.85 and safety factor, Ω, of 1.765.

3) Cold-Formed Angle Webs:

1 Based on the 1980 AISI Specification

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a. Determine Q values based on the equation given in Section 1, Part C, Item 1a.

b. Use 2005 AISC Specification Equations to determine the web available strength.

c. Use a resistance factor, φ, of 0.9 and a safety factor, Ω, of 1.67.

4) Other Cold-Formed Web Shapes:

a. Use the AISI Specifications for the calculation of nominal strength.

b.Use a resistance factor, φ, of 0.85 and safety factor, Ω, of 1.765.

D. General Remarks

1) Joist Girders shall be designed as simply-supported primary members. All

loads shall be applied through steel joists, and will be equal in magnitude and evenly spaced along the Joist Girder top chord.

2) The examples that follow indicate the general and specific data that is to be shown or is necessary for arriving at the final design.

3) Requests for clarification of points regarding either design or physical tests should be directed to the Managing Director, Technical Director or to the Consulting Engineer of the SJI.

4) Design of the end bearing is the responsibility of the applicant and is not included. Sizes of plates should not be shown.

5) Weld design is the responsibility of the applicant and weld sizes are not to be shown.

Designs of Joist Girders, submitted for Steel Joist Institute design check, must be in accordance with the Standard Specifications shown in the current edition of the Institute’s catalog. The principles involved in the design of the chords, webs and welds are explained in the accompanying material in a typical example. It is not to be inferred that the applicant must use the modified Warren configuration of the illustrative example, or panel lengths, or chord sizes used therein. The example is merely presented in order to help illustrate the general engineering principles as applied to Joist Girders which are accepted as the basis of the design by the Steel Joist Institute. An applicant submitting a design for Joist Girders must verify the chords and webs as outlined in Section 3. The stress of the top chord must be calculated at all critical panel points and mid-panel points in accordance with the Steel Joist Institute specifications. If the panel lengths are varied within a Joist Girder, panels other than the end or center may be critical.

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SECTION 2 GLOSSARY OF TERMS ASD (Allowable Strength Design). Method of proportioning structural components such that the allowable strength equals or exceeds the required strength of the component under the action of the ASD load combinations. ASD Load Combination. Load combination in the applicable building code intended for allowable strength design (allowable stress design). Allowable Strength. Nominal strength divided by the safety factor, Rn/Ω. Available Strength. Design strength or allowable strength as appropriate. Bearing. The distance that the bearing shoe or seat of a joist or Joist Girder extends over its masonry, concrete or steel support. Bridging. In general, a member connected to a joist to brace it from lateral movement. This may be horizontal bridging or diagonal bridging, as required. Buckling. Limit state of sudden change in the geometry of a structure or any of its elements under a critical loading condition. Buckling Strength. Nominal strength for buckling or instability limit states. Chords. The top and bottom members of a joist or Joist Girder. When a chord is comprised of two angles there is usually a gap between the members. Clear Span. The actual clear distance or opening between supports for a joist, that is the distance between walls or the distance between the edges of flanges of beams. Cold-Formed Steel Structural Member. Shape manufactured by press-braking blanks sheared from sheets, cut lengths of coils or plates, or by roll forming cold- or hot-rolled coils or sheets; both forming operations being performed at ambient room temperature, that is, without manifest addition of heat such as would be required for hot forming. Design Load. Applied load determined in accordance with either LRFD load combinations or ASD load combinations, whichever is applicable. Design Strength. Resistance factor multiplied by the nominal strength, φRn. Effective Length. Length of an otherwise identical column with the same strength when analyzed with pin-ended boundary conditions. End Diagonal or Web. The first web member on either end of a joist or Joist Girder which begins at the top chord at the seat and ends at the first bottom chord panel point.

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Factored Load. Product of a load factor and the nominal load. Filler. A rod, plate or angle welded between a two angle web member or between a top or bottom chord panel to tie them together, usually located at the middle of the member. Gravity Load. Load, such as that produced by dead and live loads, acting in the downward direction. Instability. Limit state reached in the loading of a structural component, frame or structure in which a slight disturbance in the loads or geometry produces large displacements. Joist. A structural load-carrying member with an open web system which supports floors and roofs utilizing hot-rolled or cold-formed steel and is designed as a simple span member. Currently, the SJI has the following joist designations: K-Series including KCS, LH-Series and DLH-Series. Joist Girder. A primary structural load-carrying member with an open web system designed as a simple span supporting equally spaced concentrated loads of a floor or roof system acting at the panel points of the member and utilizing hot-rolled or cold-formed steel. Limit State. Condition in which a structure or component becomes unfit for service and is judged either to be no longer useful for its intended function (serviceability limit state) or to have reached its ultimate load-carrying capacity (strength limit state). Load. Force or other action that results from the weight of building materials, occupants and their possessions, environmental effects, differential movement, or restrained dimensional changes. Load Effect. Forces, stresses, and deformations produced in a structural component by the applied loads. Load Factor. Factor that accounts for deviations of the nominal load from the actual load, for uncertainties in the analysis that transforms the load into a load effect, and for the probability that more than one extreme load will occur simultaneously. LRFD (Load and Resistance Factor Design). Method of proportioning structural components such that the design strength equals or exceeds the required strength of the component under the action of the LRFD load combinations. LRFD Load Combination. Load combination in the applicable building code intended for strength design (Load and Resistance Factor Design). Nominal Load. Magnitude of the load specified by the applicable building code.

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Nominal Strength. Strength of a structure or component (without the resistance factor or safety factor applied) to resist the load effects, as determined in accordance with these Standard Specifications. Required Strength. Forces, stress, and deformations produced in a structural component, determined by either structural analysis, for the LRFD or ASD load combinations, as appropriate, or as specified by these Standard Specifications. Resistance Factor, φ. Factor that accounts for unavoidable deviations of the nominal strength from the actual strength and for the manner and consequences of failure. Safety Factor, Ω. Factor that accounts for deviations of the actual strength from the nominal strength, deviations of the actual load from the nominal load, uncertainties in the analysis that transforms the load into a load effect and for the manner and consequences of failure. Service Load. Load under which serviceability limit states are evaluated. Serviceability Limit State. Limiting condition affecting the ability of a structure to preserve its appearance, maintainability, durability, or the comfort of its occupants or function of machinery, under normal usage. Slenderness Ratio. The ratio of the effective length of a column to the radius of gyration of the column about the same axis of bending. Span. The centerline-to-centerline distance between structural steel supports such as a beam, column or Joist Girder or the clear span distance plus four inches onto a masonry or concrete wall. Specified Minimum Yield Stress. Lower limit of yield stress specified for a material as defined by ASTM. Stability. Condition reached in the loading of a structural component, frame or structure in which a slight disturbance in the loads or geometry does not produce large displacements. Standard Specifications. Documents developed and maintained by the Steel Joist Institute for the design and manufacture of open web steel joists and Joist Girders. The term “SJI Standard Specifications” encompass by reference the following: ANSI/SJI-K1.1 Standard Specification for Open Web Steel Joists, K-Series;

ANSI/SJI-LH/DLH-1.1 Standard Specifications for Longspan Steel Joists, LH-Series and Deep Longspan Steel Joists, DLH-Series; and ANSI/SJI-JG-1.1 Standard Specifications for Joist Girders.

Strength Limit State. Limiting condition affecting the safety of the structure, in which the ultimate load-carrying capacity is reached.

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Tensile Strength (of material). Maximum tensile stress that a material is capable of sustaining as defined by ASTM. Webs. The vertical or diagonal members joined at the top and bottom chords of a joist or Joist Girder to form triangular patterns. Yield Point. First stress in a material at which an increase in strain occurs without an increase in stress as defined by ASTM. Yield Strength. Stress at which a material exhibits a specified limiting deviation from the proportionality of stress to strain as defined by ASTM. Yield Stress. Generic term to denote either yield point or yield strength, as appropriate for the material.

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SECTION 3 EXAMPLES OF JOIST GIRDER DESIGN CHECKS The following examples are for illustrative purposes only, and it is not to be implied that the manufacturer must follow the choice of chords, webs or even general configuration. 3.1 EXAMPLE 1A The Joist Girder designation for this example: 40G7N11.6F @ 35’-0” span; LRFD Design, Modified Warren Geometry GIVEN: Designation: 40G 7N 11.6F Length: 35.00 ft. Working Length: 34.67 ft. All Material: Fy = 50,000 psi Weld Electrode: E70XX Chord Spacing: 1 in. Back to Back Dead load 3000 lb (includes weight of girder) Live load 5000 lb Factored load 1.4 D = 4200 lb 1.2 D + 1.6 L = 11,600 lb P Resistance Factors φt = 0.90 φc = 0.90 Design Stress φtFy = 0.90 x 50 ksi = 45 ksi (Tension members) REQUIRED: fu shall not exceed φFn for all members where, fu = required stress, ksi Fn = nominal stress, ksi φ = resistance factor φFn = design stress, ksi See also, Steel Joist Institute Standard Specification for Joist Girders

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ANALYSIS and DESIGN:

PP/2 P P P P P P/2

34.670 '

4.835 ' 5.000 ' 5.000 ' 5.000 ' 5.000 ' 5.000 ' 4.835 '

d = 38.52 "

2.335 ' 2.500 '

1 2

3

4 5

6

7 8

9

10 11

12

13 14

15

16 17

18

19 20

21

22

CL

R = 3.5P R = 3.5P

Figure 1: Joist Girder Layout and Loading Calculate Moment at Midspan of Girder:

2)335.17(P)5.125.75.2(P)335.17(P5.3MCL −++−×=

lbin096,107,4kipsft26.3426.11505.29

P505.29

−=−=

×=×=

ASSUME EFFECTIVE DEPTH = d = 38 in.

2

ytd'req

.in40.2

)000,50)(9.0)(38(096,107,4

)F(dMA

=

=φ

=

TRY – T.C. – 2L 2 ½ x 2 ½ x 5/16 And TRY – B.C. – 2L 2 ½ x 2 ½ x 5/16

.in52.38)740.0740.0(40)yy(Dd BCTC

=+−=+−=

Calculate maximum B.C. force: Occurs at point directly below panel point 10.

52.382

)12)(835.14(P)12)(105(P)12)(835.14(P5.3000,1

dM 10

⎥⎦⎤

⎢⎣⎡ −+−

=

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lb622,106FORCEMAX BC =

2

yt

BC .in37.2000,50x9.0

622,106F

Force==

φ

2L 2 ½ x 2 ½ x 5/16, Area = 2.93 in.2 Therefore, trial section axial stress is OK Calculate maximum T.C. force: Occurs at panel point 11. Calculate moment at panel point 12.

lb622,106FORCEMAX TC = Trial TC section = 2L 2 ½ x 2 ½ x 5/16 Io = 0.849 in.4; A = 1.46 in.2; rx = 0.761 in.; rz = 0.489 in.; Q = 1.0 Io-o = Io + Ax2 = 0.849 + 1.46(0.5 + 0.740)2 = 3.094 in.4

.in456.11.463.094

AI

r ooyy === −

−

lz = 15 in. (TC Fillers); lx = 30 in.; ly-y = 60 in. (l/r)z = 15/0.489 = 30.67 (l/r)x = 30/0.761 = 39.42 (l/r)y-y = 60/1.456 = 41.21 Governs ≤ 90 Check critical stress:

( )

psi161,44000,50658.00.1FF

psi536,168F

rl

EF,whereF658.0QF

,use21.4143.113000,500.110x2971.4QF

E4.71

536,168)000,50(0.1

ncr

e

2

2

eyF

QF

cr

6

y

e

y

=⎥⎥⎦

⎤

⎢⎢⎣

⎡==

=

π=

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡=

∴≥=×=

⎟⎟⎠

⎞⎜⎜⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛

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Design Stress: psi745,39)161,44(9.0Fnc ==φ Required Stress:

OKpsi745,39psi514,36)in46.1(2

lb622,106f 2u ≤==

CHECK SHEAR CAPACITY OF CHORD MEMBERS

1 2

3

4

POSSIBLE SHEAR FAILURE PLANE

Figure 2. Possible Shear Failure Locations

tT or C

Vb

Figure 3. Forces on Critical Section

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CHECK BOTTOM CHORD AT PANEL POINT 3: V = Shear force across chord section, kips T = Tension force in the chord section, kips C = Compression force in the chord section, kips A = Chord area, in.2

EDL = 2.335 ft = 28.02 in. VAR = 2.500 ft = 30.00 in. PNL = 5.000 ft = 60.00 in. d = 38.52 in. b = 2.5 in. t = 0.3125 in. V = 3P = 3 x 11.6 = 34.8 kips T = V/(d/EDL) = 34.8/(38.52/28.02) = 25.3 kips A = 2.93 in.2 Required Stress: Shear fuv = V / (2*t*b) = 34.8 / (2*0.3125*2.5) = 22.27 ksi Tensile fut = T / A = 25.3 / 2.93 = 8.63 ksi Shear and Axial Stress Interaction: ( vφ = 1.0)

2uv

2utyv f4f2

1F6.0 +≥φ

OKksi68.22ksi30 ∴≥ USE 2L 2 ½ x 2 ½ x 5/16 FOR BOTTOM CHORD

CHECK TOP CHORD AT PANEL POINT 4: d = 40-2(0.740) = 38.52 in. b = 2.5 in. t = 0.3125 in. V = 3P = 3 x 11.6 = 34.8 kips C = 3P(EDL+VAR)/d = 52.4 kips A = 2.93 in.2 Required Stress: Shear fuv = V / (2*t*b) = 34.8 / (2*0.3125*2.5) = 22.27 ksi

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Compressive fuc = C / A = 52.4 / 2.93 = 17.88 ksi Shear and Axial Stress Interaction: ( vφ = 1.0)

2uv

2ucyv f4f2

1F6.0 +≥φ

OKksi00.24ksi30 ∴≥ USE 2L 2 ½ x 2 ½ x 5/16 FOR TOP CHORD

CHECK BOTTOM CHORD AT PANEL POINT 6: d = 40-2(0.740) = 38.52 in. b = 2.5 in. t = 0.3125 in. V = 2P = 2 x 11.6 = 23.2 kips T = [3P(EDL+VAR+1/2 PNL) – P(1/2 PNL)]/d = 70.5 kips A = 2.93 in.2 Required Stress: Shear fuv = V / (2*t*b) = 23.2 / (2*0.3125*2.5) = 14.85 ksi Tensile fut = T / A = 70.5 / 2.93 = 24.06 ksi Shear and Axial Stress Interaction: ( vφ = 1.0)

OKksi11.19ksi30

f4f21F6.0 2

uv2

utyv

∴≥

+≥φ

BY INSPECTION, SHEAR CAPACITY AT PANEL POINTS 7, 9, 10, AND 12 DOES NOT GOVERN DESIGN. CHECK THE BEARING CAPACITY OF THE OUTSTANDING LEG OF THE COMPRESSION CHORD OF THE JOIST GIRDER UNDER THE REACTION OF THE JOIST BEARING ON IT (Galambos, 2000).

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WEB DIAGONALOUSTANDING LEG

OF JOIST GIRDERTOP CHORD

BEARING SEAT OF STEEL JOIST

Figure 4. Joist Bearing on Joist Girder Panel Point

TC = 2L 2 ½ x 2 ½ x 5/16 t = 0.3125 in. b = 2.5 in. Q = 1.0 K-distance = 0.625 in. Pu = Factored girder panel load = 11,600 lb Adjusted T.C. force = 106,622 lb

psi514,36)in46.1(2

lb622,106f 2uTC ==

Width of joist bearing seat: g = 5.0 in. The allowable reaction is the lesser of:

⎥⎥⎦

⎤

⎢⎢⎣

⎡

φ−φφ

y

uTCpp QF

f6.1PandP

where, φ = 0.9

( ) ( )[ ]Kb66.5gKb2

FtP y

2

p −+−

=

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( ) ( )[ ]

kips3.18P

kips33.20625.05.266.55625.05.22

503125.0P

p

2

p

=φ

=−+−

×=

kips43.14500.19.0

514.366.13.18QFf6.1P

y

uTCp =⎥⎦

⎤⎢⎣⎡

××−=

⎥⎥⎦

⎤

⎢⎢⎣

⎡

φ−φ

The controlling value is 14.43 kips. The required reaction is ½ of the joist girder panel point load of 11.6 kips. Check Span/ry-y ≤ 575:

OK575286456.1

1267.34∴≤=

×

Check Bottom Chord Braces: l/ry-y ≤ 240 lmax = 240(ry-y) = 240(1.456)/12 lmax = 29.12 ft. USE ONE BC BRACE NEAR MIDSPAN Calculate Chord/Web Forces: TOP CHORD: BETWEEN PANEL POINTS 1-2; 2-4; 19-20; 20-22:

[ ]

lb314,2552.38

000,1)12)(335.2(P3d

MF 3TC

−=

==

BETWEEN PANEL POINTS 4-5; 5-7; 16-17; 17-19:

[ ]

lb485,7052.38

000,1)12)(5.2(P)12)(335.7(P3d

MF 6TC

−=

−==

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[ ]

lb588,9752.38

000,1)12)(5.75.2(P)12)(335.12(P3d

MF 9TC

−=

+−==

BETWEEN PANEL POINTS 10-11; 11-13:

[ ]

lb622,10652.38

000,1)12)(5.125.75.2(P)12)(335.17(P3d

MF 12TC

−=

++−==

BOTTOM CHORD: BETWEEN PANEL POINTS 3-6; 18-21:

[ ]

lb416,5252.38

000,1)12)(835.4(P3d

MF 4BC

+=

==


[ ]

lb554,8852.38

000,1)12)(5(P)12)(835.9(P3d

MF 7BC

+=

−==


[ ]

lb622,10652.38

000,1)12)(105(P)12)(835.14(P3d

MF 10BC

+=

+−==

WEB MEMBER FORCES: MIN SHEAR = 0.25(3.5P) = 10,150 lb BETWEEN PANEL POINTS 2-3; 5-6; 8-9; 11-12; 14-15; 17-18; 20-21: (VERTICALS) FVERT = 2% (MAX CHORD FORCE) = 0.02(106,622) = 2,132 lb

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lb048,43)000,1)(237.1)(6.11(3)CSC(VF

P3V

WEB

+==θ=

=


lb092,44)000,1)(267.1)(6.11(3)CSC(VF

P3V

WEB

−==θ=

=


lb394,29)000,1)(267.1)(6.11(2)CSC(VF

P2V

WEB

+==θ=

=


lb394,29)000,1)(267.1)(6.11(2)CSC(VF

P2V

WEB

−==θ=

=


lb697,14)000,1)(267.1)(6.11()CSC(VF

PV

WEB

+==θ=

=


lb697,14)000,1)(267.1)(6.11()CSC(VF

PV

WEB

−==θ=

=


lb860,12)000,1)(267.1)(6.11)(5.3(25.0)CSC(VF

SHEARMINP)5.3(25.0V

WEB

+==θ=

←=

20 of 60

FORCE ANALYSIS SUMMARY:

WEB MEMBER FORCES (lb) REQ’D COMP FORCE (lb)* 2-3; 5-6; 8-9; 11-12; 14-15; 17-18; 20-21

-2,132 ---

1-3; 22-21 +43,048 -10,762 3-4; 21-19 -44,092 --- 4-6; 19-18 +29,394 -7,349 6-7; 18-16 -29,394 --- 7-9; 16-15 +14,697 -3,674 9-10; 15-13 -14,697 --- 10-12; 13-12 +12,860 -3,215

*SJI Specification 1003.4 (b)

TOP CHORD FORCES (lb) 1-2; 2-4 -25,314 4-5; 5-7 -70,485 7-8; 8-10 -97,588 10-11; 11-13 -106,622 13-14; 14-16 -97,588 16-17; 17-19 -70,485 19-20; 20-22 -25,314

BOTTOM CHORD FORCES (lb) 3-6 +52,416 6-9 +88,554 9-12 +106,622 12-15 +106,622 15-18 +88,554 18-21 +52,416 --- ---

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DESIGN WEB MEMBERS: BETWEEN PANEL POINTS 2-3; 5-6; 8-9; 11-12; 14-15; 17-18; 20-21: (VERTICALS) TRY L 1 ¼ x 1 ¼ x 1/8 (crimped ends) l = 38.52 in.; rz = 0.246 in.; A = 0.297 in.2; Q = 1.0 Force = -2,132 lb fu = -2,132/0.297 = 7,178 psi (l/r)z = 38.52/0.246 = 156.59 ≤ 200 Check critical stress:

( )

psi237,10)671,11(877.0FF

psi673,11F

rl

EF,whereF877.0F

,use59.15643.113000,500.110x2971.4QF

E4.71

ncr

e

2

2

eecr

6

y

===

=

π==

∴≤=×=

Design Stress: psi213,9)237,10(9.0Fnc ==φ > fu OK use L 1 ¼ x 1 ¼ x 1/8

Weld: .in8.0)2(1392

132,2=

Use 2” of 1/8” weld each end of angle (1” min. each leg of each end)

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BETWEEN PANEL POINTS 1-3; 22-21: (End Diagonal) Design for tension:

2

ytd'req .in957.0

000,50x9.0048,43

FForceA ==φ

=

Try 2L – 1 ½ x 1 ½ x 3/16 l = 47.63 in.; rz = 0.293 in.; rx = 0.457 in.; A2L = 1.054 in.2; Q = 1.0 (l/r)z = 47.63/0.293 = 162.56 (no fillers) ≤ 240 Check compression: Force = -10,762 lb fu = -10,762/1.054 = 10,211 psi Check critical stress:

( )

psi499,9)831,10(877.0FF

psi831,10F

rl

EF,whereF877.0F

,use56.16243.113000,500.110x2971.4

ncr

e

2

2

eecr

6

===

=

π==

∴≤=×=yQF

E4.71

Design Stress: psi549,8)499,9(9.0Fnc ==φ < fu NG – Try with 1 filler. (l/r)x = 47.63/0.457 = 104.22 (One filler at mid-length)

23 of 60

Check critical stress:

( )

psi597,22FF

psi351,26F

rl

EF,whereF658.0QF

,use22.10443.113000,500.110x2971.4QF

E4.71

ncr

e

2

2

eyF

QF

cr

6

y

e

y

==

=

π=

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡=

∴>=×=

⎟⎟⎠

⎞⎜⎜⎝

⎛

Design Stress: psi337,20)597,22(9.0Fnc ==φ > fu Use 2L – 1 ½ x 1 ½ x 3/16 w/ filler

Weld: .in3.10)3(1392

048,43=

Use 5 1/4” of 3/16” weld each end of each angle BETWEEN PANEL POINTS 3-4; 21-19: (First Primary Compression Web) Try 2L – 2 x 2 x 3/16 l = 48.82 in.; rz = 0.394 in.; rx = 0.617 in.; A2L = 1.430 in.2; Q = 1.0 Force = -44,092 lb fu = -44,092/1.430 = 30,834 psi (l/r)x = 48.82/0.617 = 79.12 (One filler at mid-length) ≤ 200

24 of 60


( )

psi636,31FF

psi722,45F

rl

EF,whereF658.0QF

,use12.7943.113000,500.110x2971.4QF

E4.71

ncr

e

2

2

eyF

QF

cr

6

y

e

y

==

=

π=

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡=

∴>=×=

⎟⎟⎠

⎞⎜⎜⎝

⎛

Design Stress: psi472,28)636,31(9.0Fnc ==φ < fu N.G. Try 2L – 2 x 2 x 1/4 w/ filler Try 2L – 2 x 2 x 1/4 l = 48.82 in.; rz = 0.391 in.; rx = 0.609 in.; A2L = 1.876 in.2; Q = 1.0 Force = -44,092 lb fu = -44,092/1.876 = 23,503 psi (l/r)x = 48.82/0.609 = 80.16 (One filler at mid-length) ≤ 200 Check critical stress:

( )

psi256,31FF

psi543,44F

rl

EF,whereF658.0QF

,use16.8043.113000,500.110x2971.4QF

E4.71

ncr

e

2

2

eyF

QF

cr

6

y

e

y

==

=

π=

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡=

∴>=×=

⎟⎟⎠

⎞⎜⎜⎝

⎛

25 of 60

Design Stress: psi130,28)256,31(9.0Fnc ==φ > fu OK – Use 2L – 2 x 2 x 1/4 w/ filler

Weld: .in6.10)3(1392

092,44=

Use 5 1/2” of 3/16” weld each end of each angle BETWEEN PANEL POINTS 4-6; 19-18: Design for tension:

2

ytd'req .in653.0

000,50x9.0394,29

FForceA ==φ

=

Try 1L – 2 x 2 x 3/16 l = 48.82 in.; rz = 0.394 in.; rx = 0.617 in.; A = 0.715 in.2; Q = 1.0 (l/r)z = 48.82/0.394 = 123.91 (no fillers) ≤ 240 Check compression: Force = -7,349 lb fu = -7,349/0.715 = 10,278 psi Check critical stress:

( )

psi349,16)642,18(877.0FF

psi642,18F

rl

EF,whereF877.0F

,use91.12343.113000,500.110x2971.4QF

E71.4

ncr

e

2

2

eecr

6

y

===

=

π==

∴≤=×=

26 of 60

Design Stress: psi714,14)349,16(9.0Fnc ==φ > fu OK

Weld: .in1.7)3(1392

394,29=

Use 7 1/2” of 3/16” weld each end of angle (3 3/4” min. each leg of each angle) BETWEEN PANEL POINTS 6-7; 18-16: Try 2L – 2 x 2 x 0.143 l = 48.82 in.; rz = 0.396 in.; rx = 0.624 in.; A = 1.104 in.2; Q = 0.898 Force = -29,394 lb fu = -29,394/1.104 = 26,625 psi (l/r)x = 48.82/0.624 = 78.24 (One filler at mid-length) ≤ 200 Check critical stress:

( )

psi039,30FF

psi756,46F

rl

EF,whereF658.0QF

,use24.7870.119000,50898.010x2971.4QF

E4.71

ncr

e

2

2

eyF

QF

cr

6

y

e

y

==

=

π=

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡=

∴>=×=

⎟⎟⎠

⎞⎜⎜⎝

⎛

27 of 60


Weld: .in6.10)2(1392

394,29=


2

ytd'req .in327.0

000,50x9.0697,14

FForceA ==φ

=

Try 1L – 1 ½ x 1 ½ x 3/16 l = 48.82 in.; rz = 0.293 in.; rx = 0.457 in.; A = 0.527 in.2; Q = 1.0 (l/r)z = 48.82/0.293 = 166.62 (no fillers) ≤ 240 Check compression: Force = -3,683 lb fu = -3,683/0.527 = 6,989 psi Check critical stress:

( )

psi042,9)310,10(877.0FF

psi310,10F

rl

EF,whereF877.0F

,use62.16643.113000,500.110x2971.4

ncr

e

2

2

eecr

6

===

=

π==

∴≤=×=yQF

E4.71

28 of 60


Weld: .in5.3)3(1392

697,14=

Use 3 1/2” of 3/16” weld each end of angle (1 3/4” min. each leg of each end) BETWEEN PANEL POINTS 9-10; 15-13: Try 2L – 1 ½ x 1 ½ x 3/16 l = 48.82 in.; rz = 0.293 in.; rx = 0.457 in.; A = 1.054 in.2; Q = 1.0 Force = -14,732 lb fu = -14,732/1.054 = 13,977 psi (l/r)x = 48.82/0.457 = 106.83 (One filler at mid-length) ≤ 200 Check critical stress:

( )

psi705,21FF

psi079,25F

rl

EF,whereF658.0QF

,use83.10643.113000,500.110x2971.4QF

E4.71

ncr

e

2

2

eyF

QF

cr

6

y

e

y

==

=

π=

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡=

∴>=×=

⎟⎟⎠

⎞⎜⎜⎝

⎛

29 of 60


Weld: .in5.3)3(1392

697,14=

Use 2” of 3/16” weld each end of each angle BETWEEN PANEL POINTS 10-12; 13-12: Design for tension:

2

ytd'req .in286.0

000,50x9.0860,12

FForceA ==φ

=

Try 1L – 1 ½ x 1 ½ x 5/32 l = 48.82 in.; rz = 0.295 in.; rx = 0.461 in.; A = 0.444 in.2; Q = 1.0 (l/r)z = 48.82/0.295 = 165.49 ≤ 240 Check compression: Force = -3,215 lb fu = -3,215/0.444 = 7,241 psi Check critical stress:

( )

psi166,9)451,10(877.0FF

psi451,10F

rl

EF,whereF877.0F

,use49.16543.113000,500.110x2971.4QF

E71.4

ncr

e

2

2

eecr

6

y

===

=

π==

∴≤=×=

30 of 60


Weld: .in6.4)2(1392

860,12=

Use 5” of 1/8” weld each end of angle (2 1/2” min. each leg of each end) The design submittal shall provide details to demonstrate how the required weld length will be applied, as shown in Figures 5 and 6 below.

WEB1 - 3

WEB1 - 3

WEB3 - 4

WEB2 - 3

TOP CHORD

BOTTOM CHORD

A A

Figure 5. Welding of Web Members

(For illustrative purposes only; all joist connections must be shown)

31 of 60

1" MIN WELD LENGTH

CHORD

CHORD

Figure 6. Section A – A

DEFLECTION CHECK LJG = 35’ (34.67’ working length); Assume joists are 40 ft. long. Live Load = 25 psf; 25 x 40 = 1.0 kip/ft LL Deflection at 1/360 of working length = 34.67 x 12 / 360 = 1.16”

BT

2BT

BTJG AAdAAIII

+××

++=

IT = 0.849 in.4

IB = 0.849 in.4 AT = 2.93 in.2

AB = 2.93 in.2

d = 38.52 in. IJG = 2,177 in.4

( )( )( ) ( ) ( )( )177,2000,29384

1267.34121515.1

EI384LW515.1DEFLECTION

4

JG

4

××

×⎟⎠⎞

⎜⎝⎛

==

OK.in16.1.in59.0DEFLECTION <=

32 of 60

TOP CHORD FILLERS: (if needed) Check for required weld length Given: E70XX Electrodes Angle type filler (3/16” Material) Assume 3/16 in. fillet weld Fexx = 70,000 psi φw = 0.75 Fnw = 0.6 Fexx Lw = required length of weld, in. P = chord force, lb Dw = weld size, in. φwFnweld= weld design stress = 31,500 psi fuweld = required force of weld in shear = 2% of P P = 106,622 lb fuweld = 106,622 x 0.02 = 2,132 lb

Lw = .in509.0188.0500,31

132,2414.1DF

f2

wnweldw

uweld =××

=×φ

Use 2 – 3/16” welds 3/4” long (one weld on each chord angle)* * NOTE: Minimum allowable weld length is four times the weld thickness. Weld length for web fillers and/or ties must be calculated using same procedure.

33 of 60

3.2 EXAMPLE 1B The Joist Girder designation for this example: 40G7N8K @ 35’-0” span; ASD Design, Modified Warren Geometry GIVEN: Designation: 40G 7N 8K Length: 35.00 ft. Working Length: 34.67 ft. All Material: Fy = 50,000 psi Weld Electrode: E70XX Chord Spacing: 1” Back to Back Dead load 3000 lb (includes weight of girder) Live load 5000 lb Allowable Stress Fn/Ω = 0.6Fn= 0.6Fy= 30 ksi (Tension members) REQUIRED: f shall not exceed Fn/Ω for all members where, f = required stress, ksi Fn = nominal stress, ksi Ω = safety factor Fn/Ω = 0.6Fn = allowable stress See also, Steel Joist Institute Standard Specification for Joist Girders

34 of 60

ANALYSIS and DESIGN:

PP/2 P P P P P P/2

34.670 '

4.835 ' 5.000 ' 5.000 ' 5.000 ' 5.000 ' 5.000 ' 4.835 '

d = 38.52 "

2.335 ' 2.500 '

1 2

3

4 5

6

7 8

9

10 11

12

13 14

15

16 17

18

19 20

21

22

CL

R = 3.5P R = 3.5P

Figure 1: Joist Girder Layout and Loading Calculate Moment at Midspan of Girder: Where, P = 8.0 kips

2)335.17(P)5.125.75.2(P)335.17(P5.3MCL −++−×=

lbin480,832,2kipsft04.236

8505.29P505.29

−=−=

×=×=

ASSUME EFFECTIVE DEPTH = d = 38 in.

2

yd'req

.in48.2

)000,50)(6.0)(38(480,832,2

)F6.0(dMA

=

==

TRY – T.C. – 2L 2 ½ x 2 ½ x 5/16 And TRY – B.C. – 2L 2 ½ x 2 ½ x 5/16

.in52.38)740.0740.0(40)yy(Dd BCTC

=+−=+−=

35 of 60

Calculate maximum B.C. force: Occurs at point directly below panel point 10.

52.382

)12)(835.14(P)12)(105(P)12)(835.14(P5.3000,1

dM10

⎥⎦⎤

⎢⎣⎡ −+−

=

lb533,73FORCEMAX BC =

2

y

BC .in45.2)000,50(6.0

533,73F6.0

Force==

2L 2 ½ x 2 ½ x 5/16, Area = 2.93 in.2 Therefore, trial section axial stress is OK Calculate maximum T.C. force: Occurs at panel point 11. Calculate moment at panel point 12.

lb533,73FORCEMAX TC = Trial TC section = 2L 2 ½ x 2 ½ x 5/16 Io = 0.849 in.4; A = 1.46 in.2; rx = 0.761 in.; rz = 0.489 in.; Q = 1 Io-o = Io + Ax2 = 0.849 + 1.46(0.5 + 0.740)2 = 3.094 in.4

.in456.11.463.094

AI

r ooyy === −

−

lz = 15 in. (TC Fillers); lx = 30 in.; ly-y = 60 in. (l/r)z = 15/0.489 = 30.67 (l/r)x = 30/0.761 = 39.42 (l/r)y-y = 60/1.456 = 41.21 Governs ≤ 90

36 of 60


( )

psi161,44000,50658.00.1FF

psi536,168F

rl

EF,whereF658.0QF

,use21.4143.113000,500.110x2971.4QF

E4.71

536,168000,50(0.1

ncr

e

2

2

eyF

QF

cr

6

y

e

y

=⎥⎥⎦

⎤

⎢⎢⎣

⎡==

=

π=

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡=

∴≥=×=

⎟⎟⎠

⎞⎜⎜⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛

Allowable Stress: psi497,26)161,44(6.0F6.0 n == Required Stress:

psi183,25)in46.1(2

lb533,73f 2 ==

.OKisStressAxialSectionTrialF6.0f n ∴≤

37 of 60

CHECK SHEAR CAPACITY OF CHORD MEMBERS

1 2

3

4

POSSIBLE SHEAR FAILURE PLANE

Figure 2. Possible Shear Failure Locations

tT or C

Vb

Figure 3. Forces on Critical Section

38 of 60

CHECK BOTTOM CHORD AT PANEL POINT 3: V = Shear force across chord section, kips T = Tension force in the chord section, kips C = Compression force in the chord section, kips A = Chord area, in.2

EDL = 2.335 ft = 28.02 in. VAR = 2.500 ft = 30.00 in. PNL = 5.000 ft = 60.00 in. d = 40-2(0.740) = 38.52 in. b = 2.5 in. t = 0.3125 in. V = 3P = 3 x 8.0 = 24.0 kips T = V/(d/EDL) = 24.0/(38.52/28.02) = 17.5 kips A = 2.93 in.2 Required Stress: Shear fv = V / (2*t*b) = 24 / (2*0.3125*2.5) = 15.36 ksi Tensile ft = T / A = 17.5 / 2.93 = 5.97 ksi Shear and Axial Stress Interaction ( )5.1v =Ω

OKksi65.15ksi20

f4f21/F6.0 2

v2

tvy

∴≥

+≥Ω

CHECK TOP CHORD AT PANEL POINT 4: b = 2.5 in. t = 0.3125 in. V = 3P = 3 x 8.0 = 24.0 kips C = 3P(EDL+VAR)/d = 36.15 kips A = 2.93 in.2 Required Stress: Shear fv = V / (2*t*b) = 24.0 / (2*0.3125*2.5) = 15.36 ksi Compressive fc = C / A = 36.15 / 2.93 = 12.34 ksi

39 of 60

Shear and Axial Stress Interaction ( )5.1v =Ω

OKksi55.15ksi20

f4f21/F6.0 2

v2

cvy

∴≥

+≥Ω

CHECK BOTTOM CHORD AT PANEL POINT 6: d = 40-2(0.740) = 38.52 in. b = 2.5 in. t = 0.3125 in. V = 2P = 2 x 8.0 = 16.0 kips T = [3P(EDL+VAR+1/2 PNL) – P(1/2 PNL)]/d = 48.61 kips A = 2.93 in.2 Required Stress: Shear fv = V / (2*t*b) = 16.0 / (2*0.3125*2.5) = 10.24 ksi Tensile ft = T / A = 48.61 / 2.93 = 16.59 ksi Shear and Axial Stress Interaction ( )5.1v =Ω

OKksi18.13ksi20

f4f21/F6.0 2

v2

cvy

∴≥

+≥Ω

BY INSPECTION, SHEAR CAPACITY AT PANEL POINTS 7, 9, 10, AND 12 DOES NOT GOVERN DESIGN. CHECK THE BEARING CAPACITY OF THE OUTSTANDING LEG OF THE COMPRESSION CHORD OF THE JOIST GIRDER UNDER THE REACTION OF THE JOIST BEARING ON IT (Galambos, 2000).

40 of 60

WEB DIAGONALOUSTANDING LEG

OF JOIST GIRDERTOP CHORD

BEARING SEAT OF STEEL JOIST

Figure 4. Joist Bearing on Joist Girder Panel Point

TC = 2L 2 ½ x 2 ½ x 5/16 t = 0.3125 in. b = 2.5 in. Q = 1.0 K-distance = 0.625 in. P = 8,000 lb

psi183,25)in46.1(2

lb533,73f 2TC ==

Width of joist bearing seat: g = 5.0 in. The allowable reaction is the lesser of:

⎥⎥⎦

⎤

⎢⎢⎣

⎡−

y

TCpp QF6.0

f6.1P6.0andP6.0

( ) ( )[ ]Kb66.5gKb2

FtP y

2

p −+−

=

41 of 60

( ) ( )[ ]

kips20.12P6.0

kips33.20625.05.266.55625.05.22

503125.0P

p

2

p

=

=−+−

×=

kips28.9500.16.0

183.256.120.12QF6.0

f6.1P6.0y

TCp =⎥⎦

⎤⎢⎣⎡

××−=

⎥⎥⎦

⎤

⎢⎢⎣

⎡−

The controlling value is 9.28 kips. The required reaction is ½ of the joist girder panel point load of 8.0 kips. 4.0 kips < 9.28 kips Therefore, the top chord angle is OK. Check Span/ry-y ≤ 575:

OK575286456.1

1267.34∴≤=

×

Check Bottom Chord Braces: l/ry-y ≤ 240 lmax = 240(ry-y) = 240(1.456)/12 lmax = 29.12 ft. USE ONE BC BRACE NEAR MIDSPAN Calculate Chord/Web Forces: TOP CHORD: BETWEEN PANEL POINTS 1-2; 2-4; 19-20; 20-22:

[ ]

lb458,1752.38

000,1)12)(335.2(P3d

MF 3TC

−=

==


[ ]

lb611,4852.38

000,1)12)(5.2(P)12)(335.7(P3d

MF 6TC

−=

−==

42 of 60


[ ]

lb302,6752.38

000,1)12)(5.75.2(P)12)(335.12(P3d

MF 9TC

−=

+−==


[ ]

lb533,7352.38

000,1)12)(5.125.75.2(P)12)(335.17(P3d

MF 12TC

−=

++−==

BOTTOM CHORD: BETWEEN PANEL POINTS 3-6; 18-21:

[ ]

lb150,3652.38

000,1)12)(835.4(P3d

MF 4BC

+=

==


[ ]

lb072,6152.38

000,1)12)(5(P)12)(835.9(P3d

MF 7BC

+=

−==


[ ]

lb533,7352.38

000,1)12)(105(P)12)(835.14(P3d

MF 10BC

+=

+−==

WEB MEMBER FORCES: MIN SHEAR = 0.25(3.5P) = 7,000 lb BETWEEN PANEL POINTS 2-3; 5-6; 8-9; 11-12; 14-15; 17-18; 20-21: (VERTICALS) FVERT = 2% (MAX CHORD FORCE) = 0.02(73,533) = 1,471 lb

43 of 60


lb688,29)000,1)(237.1)(8(3)CSC(VF

P3V

WEB

+==θ=

=


lb408,30)000,1)(267.1)(0.8(3)CSC(VF

P3V

WEB

−==θ=

=


lb272,20)000,1)(267.1)(0.8(2)CSC(VF

P2V

WEB

+==θ=

=


lb272,20)000,1)(267.1)(0.8(2)CSC(VF

P2V

WEB

−==θ=

=


lb136,10)000,1)(267.1)(0.8()CSC(VF

PV

WEB

+==θ=

=


lb136,10)000,1)(267.1)(0.8()CSC(VF

PV

WEB

−==θ=

=


lb869,8)000,1)(267.1)(0.8)(5.3(25.0)CSC(VF

SHEARMINP)5.3(25.0V

WEB

+==θ=

←=

44 of 60

FORCE ANALYSIS SUMMARY:

WEB MEMBER FORCES (lb) REQ’D COMP FORCE (lb)* 2-3; 5-6; 8-9; 11-12; 14-15; 17-18; 20-21

-1,471 ---

1-3; 22-21 +29,688 -7,422 3-4; 21-19 -30,408 --- 4-6; 19-18 +20,272 -5,068 6-7; 18-16 -20,272 --- 7-9; 16-15 +10,136 -2,534 9-10; 15-13 -10,136 --- 10-12; 13-12 +8,869 -2,217

*SJI Specification 1003.4 (b)

TOP CHORD FORCES (lb) 1-2; 2-4 -17,458 4-5; 5-7 -48,611 7-8; 8-10 -67,302 10-11; 11-13 -73,533 13-14; 14-16 -67,302 16-17; 17-19 -48,611 19-20; 20-22 -17,458

BOTTOM CHORD FORCES (lb) 3-6 +36,150 6-9 +61,072 9-12 +73,533 12-15 +73,533 15-18 +61,072 18-21 +36,150 --- ---

45 of 60

DESIGN WEB MEMBERS: BETWEEN PANEL POINTS 2-3; 5-6; 8-9; 11-12; 14-15; 17-18; 20-21: (VERTICALS) TRY L 1 ¼ x 1 ¼ x 1/8 (crimped ends) l = 38.52 in.; rz = 0.246 in.; A = 0.297 in.2; Q = 1.0 Force = -1,471 lb f = -1,471/0.297 = -4,953 psi (l/r)z = 38.52/0.246 = 156.59 ≤ 200 Check critical stress:

( )

psi237,10)673,11(877.0FF

psi673,11F

rl

EF,whereF877.0F

,use59.15643.113000,500.110x2971.4

ncr

e

2

2

eecr

6

===

=

π==

∴≤=×=yQF

E4.71

Allowable Stress: psi142,6)237,10(6.0F6.0 n == > f OK use L 1 ¼ x 1 ¼ x 1/8

Weld: .in8.0)2(928

471,1=


46 of 60

BETWEEN PANEL POINTS 1-3; 22-21: (End Diagonal) Design for tension:

2

nd'req .in990.0

)000,50(6.0712,29

F6.0ForceA ===

Try 2L – 1 ½ x 1 ½ x 3/16 l = 47.63 in.; rz = 0.293 in.; rx = 0.457 in.; A2L = 1.054 in.2; Q = 1.0 (l/r)z = 47.63/0.293 = 162.56 (no fillers) ≤ 240 Check compression: Force = -7,422 lb f = -7,422/1.054 = 7,042 psi Check critical stress:

( )

psi499,9)831,10(877.0FF

psi831,10F

rl

EF,whereF877.0F

,use56.16243.113000,500.110x2971.4

ncr

e

2

2

eecr

6

===

=

π==

∴≤=×=yQF

E4.71

Allowable Stress: psi699,5)499,9(6.0F6.0 n == < f NG – Try with 1 filler. (l/r)x = 47.63/0.457 = 104.22 (One filler at mid-length)

47 of 60


( )

psi597,22FF

psi351,26F

rl

EF,whereF658.0QF

,use22.10443.113000,500.110x2971.4QF

E4.71

ncr

e

2

2

eyF

QF

cr

6

y

e

y

==

=

π=

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡=

∴>=×=

⎟⎟⎠

⎞⎜⎜⎝

⎛

Allowable Stress: psi558,13)597,22(6.0F6.0 n == > f Use 2L – 1 ½ x 1 ½ x 3/16 w/ filler

Weld: .in7.10)3(928

688,29=

Use 5 1/2” of 3/16” weld each end of each angle BETWEEN PANEL POINTS 3-4; 21-19: (First Primary Compression Web) Try 2L – 2 x 2 x 3/16 l = 48.82 in.; rz = 0.394 in.; rx = 0.617 in.; A2L = 1.430 in.2; Q = 1.0 Force = -30,408 lb f = -30,408/1.430 = 21,264 psi (l/r)x = 48.82/0.617 = 79.12 ≤ 200 (One filler at mid-length)

48 of 60


( )

psi636,31FF

psi722,45F

rl

EF,whereF658.0QF

,use12.7943.113000,500.110x2971.4QF

E4.71

ncr

e

2

2

eyF

QF

cr

6

y

e

y

==

=

π=

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡=

∴>=×=

⎟⎟⎠

⎞⎜⎜⎝

⎛

Allowable Stress: psi982,18)636,31(6.0F6.0 n == < f N.G. Try 2L – 2 x 2 x 1/4 w/ filler l = 48.82 in.; rz = 0.391 in.; rx = 0.609 in.; A2L = 1.876 in.2; Q = 1.0 Force = -30,408lb f = -30,408/1.876 = 16,209 psi (l/r)x = 48.82/0.609 = 80.16 (One filler at mid-length) ≤ 200 Check critical stress:

( )

psi256,31FF

psi543,44F

rl

EF,whereF658.0QF

,use16.804.113000,500.110x2971.4QF

E71.4

ncr

e

2

2

eyF

QF

cr

6

y

e

y

==

=

π=

⎥⎥⎦

⎤

⎢⎢⎣

⎡=

∴>=×=

⎟⎟⎠

⎞⎜⎜⎝

⎛

49 of 60

Allowable Stress: psi754,18)256,31(6.0F6.0 n == > f OK – Use 2L – 2 x 2 x 1/4 w/ filler

Weld: .in9.10)3(928

408,30=


2

yd'req .in676.0

)000,50(6.0272,20

F6.0ForceA ===

Try 1L – 2 x 2 x 3/16 l = 48.82 in.; rz = 0.394 in.; rx = 0.617 in.; A = 0.715 in.2; Q = 1.0 (l/r)z = 48.82/0.394 = 123.91 ≤ 240 (no fillers) Check compression: Force = -5,068 lb f = -5,068/0.715 = 7,088 psi Check critical stress:

( )

psi349,16)642,18(877.0FF

psi642,18F

rl

EF,whereF877.0F

,use91.12343.113000,500.110x2971.4QF

E71.4

ncr

e

2

2

eecr

6

y

===

=

π==

∴≤=×=

50 of 60

Allowable Stress: psi809,9)349,16(6.0F6.0 n == >f OK

Weld: .in3.7)3(928

272,20=

Use 7 1/2” of 3/16” weld each end of angle (3 3/4” min. each leg of each end) BETWEEN PANEL POINTS 6-7; 18-16: Try 2L – 2 x 2 x 0.163 l = 48.82 in.; rz = 0.396 in.; rx = 0.621 in.; A = 1.25 in.2; Q = .952 Force = -20,272 lb f = -20,272/1.25 = 16,218 psi (l/r)x = 48.82/0.621 = 78.62 ≤ 200 (One filler at mid-length) Check critical stress:

( )

psi956,30FF

psi305,46F

rl

EF,whereF658.0QF

,use62.7826.116000,50952.10x2971.4QF

E4.71

ncr

e

2

2

eyF

QF

cr

6

y

e

y

==

=

π=

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡=

∴>=×=

⎟⎟⎠

⎞⎜⎜⎝

⎛

Allowable Stress: psi574,18)956,30(6.0F6.0 n == > f OK

Weld: .in9.10)2(928

272,20=

Use 5 1/2” of 1/8” weld each end of each angle

51 of 60

BETWEEN PANEL POINTS 7-9; 16-15: Design for tension:

2

yd'req .in338.0

)000,50(6.0136,10

F6.0ForceA ===

Try 1L – 1 ½ x 1 ½ x 3/16 l = 48.82 in.; rz = 0.293 in.; rx = 0.457 in.; A = 0.527 in.2; Q = 1.0 (l/r)z = 48.82/0.293 = 166.62 ≤ 240 Check compression: Force = -2,534 lb f = -2,534/0.527 = 4,808 psi Check critical stress:

( )

psi042,9)310,10(877.0FF

psi310,10F

rl

EF,whereF877.0F

,use62.16643.113000,500.110x2971.4QF

E71.4

ncr

e

2

2

eecr

6

y

===

=

π==

∴≤=×=


Weld: .in6.3)3(928

136,10=


52 of 60

BETWEEN PANEL POINTS 9-10; 15-13: Try 2L – 1 ½ x 1 ½ x 3/16 l = 48.82 in.; rz = 0.293 in.; rx = 0.457 in.; A = 1.054 in.2; Q = 1.0; Force = -10,136 lb f = -10,136/1.054 = 9,617 psi (l/r)x = 48.82/0.457 = 106.83 (One filler at mid-length) ≤ 200 Check critical stress:

( )

psi705,21FF

psi079,25F

rl

EF,whereF658.0QF

,use83.10643.113000,500.110x2971.4QF

E4.71

ncr

e

2

2

eyF

QF

cr

6

y

e

y

==

=

π=

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡=

∴>=×=

⎟⎟⎠

⎞⎜⎜⎝

⎛

Allowable Stress: psi023,13)705,21(6.0F6.0 n == > f OK

Weld: .in6.3)3(928

136,10=

Use 2” of 3/16” weld each end of each angle BETWEEN PANEL POINTS 10-12; 13-12: Design for tension:

2

yd'req .in296.0

)000,50(6.0869,8

F6.0ForceA ===

53 of 60

Try 1L – 1 ½ x 1 ½ x 5/32 l = 48.82 in.; rz = 0.295 in.; rx = 0.461 in.; A = 0.444 in.2; Q = 1.0 (l/r)z = 48.82/0.295 = 165.49 ≤ 240 Check compression: Force = -2,217 lb f = -2,217/0.444 = 4,993 psi Check critical stress:

( )

psi166,9)451,10(877.0FF

psi451,10F

rl

EF,whereF877.0F

,use49.16543.113000,500.110x2971.4QF

E71.4

ncr

e

2

2

eecr

6

y

===

=

π==

∴≤=×=


Weld: .in8.4)2(928

869,8=

Use 5” of 1/8” weld each end of angle (2 1/2” min. each leg of each end)

54 of 60

The design submittal shall provide details to demonstrate how the required weld length will be applied, as shown in Figures 5 and 6 below.

WEB1 - 3

WEB1 - 3

WEB3 - 4

WEB2 - 3

TOP CHORD

BOTTOM CHORD

A A

Figure 5. Welding of Web Members

(For illustrative purposes only; all joist connections must be shown)

1" MIN WELD LENGTH

CHORD

CHORD

Figure 6. Section A – A

55 of 60

DEFLECTION CHECK LJG = 35’ (34.67’ working length); Assume joists are 40’ long. Live Load = 25 psf; 25 x 40 = 1.0 kip/ft LL Deflection at 1/360 of working length= 34.67 x 12 / 360 = 1.16”

BT

2BT

BTJG AAdAAIII

+××

++=

IT = 0.849 in.4

IB = 0.849 in.4 AT = 2.93 in.2

AB = 2.93 in.2

d = 38.52 in. IJG = 2,177 in.4

( )( )( ) ( ) ( )( )177,2000,29384

1267.34121515.1

EI384LW515.1DEFLECTION

4

JG

4

××

×⎟⎠⎞

⎜⎝⎛

==

OK.in16.1.in59.0DEFLECTION <=

56 of 60

TOP CHORD FILLERS: (if needed) Check for required weld length Given: E70XX Electrodes Angle type filler (3/16” Material) Assume 3/16 in. fillet weld Fexx = 70,000 psi Ωw = 2.0 Fnw = 0.6 Fexx Lw = required length of weld, in. P = chord force, lb Dw = weld size, in. Fnweld/Ωw = weld allowable stress = 21,000 psi fweld = required force of weld in shear = 2% of P P = 73,533 lb fweld = 73,533 x 0.02 = 1,471 lb

Lw = ( ) .in527.0188.0000,21

471,1414.1D/F

f2

wwnweld

weld =××

=×Ω

Use 2 – 3/16” welds 3/4” long (one weld on each chord angle)* * NOTE: Minimum allowable weld length is four times the weld thickness. Weld length for web fillers and/or ties must be calculated using same procedure.

57 of 60

3.3 REFERENCES Galambos, T.V. (2000) Joists Bearing on Joist Girders: The Performance and Design Checking of the Chord-Angle Legs in Joist Girders, Department of Civil and Mineral Engineering, University of Minnesota, Minneapolis, MN, Structural Engineering Section Report No.1, January 1983, Revised January, 2000.

58 of 60

SECTION 4 PRESENTATION OF ENGINEERING DATA The preceding examples are intended to illustrate the methods of calculating and presenting the final design information for an SJI design check. For purposes of clarity, typical Joist Girders have been shown throughout. Joist Girder configurations differ and a literal interpretation of the design procedures and final presentation must be supplemented by the realization that the end result is to be a complete description of the Joist Girder, in terms of geometry and strength. Hence, all tables and drawings submitted for approval must represent the Joist Girder of the applicant, which might be comprised of cold-formed sections, hot rolled angles top and bottom, have variations in web systems, or be of some basic configuration other than the modified Warren truss system. For example, if the 40G7N8K Joist Girder chosen herein had a structural tee for the bottom chord instead of angles, all tables and drawings submitted would have to reflect the particular situation of the applicant’s design. Submittal for the Steel Joist Institute approval must contain the following information for the use of the Consulting Engineer in checking, as well as for the files in the SJI headquarters and Consulting Engineer’s office:

A) A table of all relevant cross-sectional properties of sections to be used for chords and webs, a drawing with all relevant information concerning the geometric configuration (e.g. panel spacing and panel configuration, truss type, etc.) and a table giving such information as: distance between chord angles, weld size (as they relate to angle thickness), electrode grade, weld configuration details, and details of the web-to-chord joint.

B) A description of the logic used in preparing the design program, and a detailed listing of the design program annotated with appropriate comments to indicate where each of the relevant requirements of the Standard Specification are complied with. Comments relating to the structural analysis, to the scheme of iterating to the final selection of members and to the assumptions used, shall be provided.

C) As a minimum, an ASD design for each of the following “K” designations and lengths, and an LRFD design for each of the following “F” designations and lengths:

40G6N12K 40 ft. 40G6N18F 40 ft. 40G7N12K 40 ft. 40G7N18F 40 ft. 40G8N12K 40 ft. 40G8N18F 40 ft. 40G4N56K 35 ft. 40G4N84F 35 ft. 84G16N12K 80 ft. 84G16N18F 80 ft.

59 of 60

Additional designs may be requested by the Consulting Engineer, or may be required if the above listed designations do not reflect all typical geometric configurations or types of construction. Welding data must be included. This information may be presented in the form of tables or a computer printout. The format for presenting the design data must be properly labeled and sufficiently detailed so that all relevant checking steps can be readily identified and verified by manual calculation.

D) A complete design example of the above Joist Girder illustrating in detail

the methods or procedures and logic used to arrive at the figures presented in the tables or on the computer printout.

E) A statement that the design program was prepared in accordance with the

“SJI Standard Specifications” of latest adoption by a registered professional engineer or by a person under the close supervision of a registered professional engineer. The signature and seal of this professional engineer must be included with the design submittal.

The Consulting Engineer of the Steel Joist Institute will verify that the Joist Girder design scheme submitted will produce designs which fulfill all requirements of the SJI Standard Specifications, and this will be stated in the recommendation for approval. In order to expedite the approval process it is desirable to arrange for a personal interview between the Consulting Engineer and the professional engineer preparing the design program. The member company will be responsible for updating their designs in accordance with specification changes. The revised design must be approved within eighteen months, or as otherwise specified by the Board of Directors, or written notification from the Managing Director of the required change. The Steel Joist Institute retains the right to require any member company with a design to submit a complete design of any Joist Girder designation at any time. This design may be for any increment of span between the limits shown in the applicable Design Guide Weight Table for Joist Girders. The design information must be available to the SJI headquarters within 24 hours after notification is received by the member company concerned.

60 of 60

Notes Regarding Presentation of Data 1. A Chord Properties Table must be submitted with the design data. For

nonstandard shapes such as cold-formed sections, not only must the geometric properties be shown, but also all dimensions necessary to describe the sections.

2. All dimensions such as the radii of bends, the distance from the end of the joist to

the center of the bend of the end bar, E0, and others, must be clearly indicated. 3. The clearances from the outside surface of the chords to the back of the web bend

must be indicated for all joists. 4. Wherever the framing of a joint is too complex to be clearly defined, large scale

drawings must be submitted.

5. An example calculation for the design of a joist girder must accompany the design submittal. The specific joist girder designation will be chosen by the SJI Consulting Engineer.

Computer Format Presentation Summary The following shall be submitted:

1. A description of the program

2. Example printouts of one design length in both LRFD and ASD for each designation:

a. Member sizes and properties b. Dimensions c. Required force (Fu) and allowable force (Fa) for each member if it is a

LRFD or ASD design, respectively d. Check for bottom chord braces e. Joint eccentricities f. Combined stress check g. Deflection check h. Filler Table

3. Properly dimensioned drawings of Joist Girder configurations, end details and

accessories

4. Cover letter affixed with P.E. Stamp