lrfd slab bridge design check
TRANSCRIPT
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LRFD Slab Bridge Design, V1.2 Check Page 1 of 34Completed by Kurt Heidenreich, P.E., S.E., KJH Consulting, LLC
LRFD Slab Bridge Design Software, Version 1.2
Design Example Check
This example check is provided to assist the designer in understanding the key program functions andassociated design calculations. This is intended to be a sample to guide the designer to complete more
detailed checks if desired. For this example, a three span (30,40,30) continuous flat slab was selected.The end bents are cap type supports and the interior piers are wall type supports.
The bridge cross section consists of a two lane roadway with shoulders and 18 inch barrier railing on eachside. Based on the calculation Roadway/12, the code indicates a 3 lane bridge. However, we have
overridden this calculation and specified a 2 lanes bridge.
For this example, the railing weighs 400 plf, and a future wearing surface of 35 psf was used. For
simplicity of calculations, the bridge is not skewed. The other bridge properties and materials are
presented in the printout.
LIVE LOAD
Only standard HL-93 loading (no special vehicles) will be used to make the comparison easier for liveloading. The Washington State Department of Transportation, Bridge and Structures Office,
QConBridge Version 1.0 software package was used to compare the live load results. This program uses
the metric version to analyze a bridge and then soft converts to the English equivalent. Therefore, sincethe metric and English versions use different load values and dimensions, the results do not match
exactly. The metric equivalent axle load is 145KN (32.6 kips) which is about 2% higher than the English
version, but the lane load is 9.3N/mm (637 plf) instead of 640 plf, which is 0.5% lower.
The maximum positive HL-93 moment, at the center of span 2, is 452.38 ft-k compared to -449.46 ft-k
from Qcon, and negative moment, at support 2, is -378.96 ft-k compared to -381.96 ft-k from Qcon. This
difference is within 1%, which considering the soft conversion is very close.
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LRFD Slab Bridge Design, V1.2 Check Page 2 of 34Completed by Kurt Heidenreich, P.E., S.E., KJH Consulting, LLC
Qcon HL-93 summary output table for a three span (30, 40 30) continuous superstructure with pinned
supports is provided below.
Live Load Envelopes (Per Lane)
Span Point Min Shear(lbs) Max Shear(lbs)Min Moment(ft-lbs)Max Moment(ft-lbs)
1 0 -10.691e+03 71.788e+03 0.000e+00 0.000e+001 1 -10.809e+03 59.767e+03 -32.074e+03 181.815e+03
1 2 -17.315e+03 50.003e+03 -64.149e+03 308.672e+03
1 3 -24.034e+03 41.047e+03 -96.224e+03 385.777e+03
1 4 -30.270e+03 32.651e+03 -128.299e+03 415.433e+03
1 5 -38.623e+03 24.899e+03 -160.374e+03 408.873e+03
1 6 -46.847e+03 17.848e+03 -192.449e+03 373.271e+03
1 7 -54.767e+03 11.638e+03 -224.524e+03 300.246e+03
1 8 -64.813e+03 6.314e+03 -256.599e+03 196.435e+03
1 9 -74.742e+03 3.003e+03 -296.787e+03 83.649e+03
1 10 -83.906e+03 1.999e+03 -381.956e+03 59.990e+03
2 0 -6.748e+03 85.609e+03 -381.956e+03 59.990e+03
2 1 -6.839e+03 77.379e+03 -211.219e+03 98.826e+03
2 2 -9.354e+03 65.107e+03 -156.300e+03 231.477e+03
2 3 -16.128e+03 53.079e+03 -132.294e+03 353.586e+03
2 4 -24.168e+03 42.243e+03 -109.559e+03 428.574e+03
2 5 -32.976e+03 32.976e+03 -86.824e+03 449.463e+03
2 6 -42.243e+03 24.168e+03 -109.559e+03 428.574e+032 7 -53.079e+03 16.128e+03 -132.294e+03 353.586e+03
2 8 -65.107e+03 9.354e+03 -156.300e+03 231.477e+03
2 9 -77.379e+03 6.839e+03 -211.219e+03 98.826e+03
2 10 -89.085e+03 6.748e+03 -381.956e+03 59.990e+03
3 0 -1.999e+03 81.806e+03 -381.956e+03 59.990e+03
3 1 -3.003e+03 74.742e+03 -296.787e+03 83.649e+03
3 2 -6.314e+03 64.813e+03 -256.599e+03 196.435e+03
3 3 -11.638e+03 54.767e+03 -224.524e+03 300.246e+03
3 4 -17.848e+03 46.847e+03 -192.449e+03 373.271e+03
3 5 -24.899e+03 38.623e+03 -160.374e+03 408.873e+03
3 6 -32.651e+03 30.270e+03 -128.299e+03 415.433e+03
3 7 -41.047e+03 24.034e+03 -96.224e+03 385.777e+03
3 8 -50.003e+03 17.315e+03 -64.149e+03 308.672e+03
3 9 -59.767e+03 10.809e+03 -32.074e+03 181.815e+03
3 10 -71.788e+03 10.691e+03 0.000e+00 0.000e+00
Live Load Envelopes (Per Lane)
Pier FxMin(lbs) FxMax(lbs) FyMin(lbs) FyMax(lbs) MzMin(ft-lbs) MzMax(ft-lbs)
1 0.000e+00 0.000e+00 -10.691e+03 71.788e+03 0.000e+00 0.000e+00
2 0.000e+00 0.000e+00 -8.748e+03 112.848e+03 0.000e+00 0.000e+00
3 0.000e+00 0.000e+00 -8.748e+03 112.848e+03 0.000e+00 0.000e+00
4 0.000e+00 0.000e+00 -10.691e+03 71.788e+03 0.000e+00 0.000e+00
The HL-93 reaction at support 1 is 70.89 k compared to 71.79 k for Qcon, and 111.74 k at support 2
compared to 112.85 k for Qcon. The minimum live load reaction at support 1 is -10.60 k compared to -
10.69 k, and -8.65 k at support 2 compared to -8.74 k for Qcon. Again these values are about 1%
different due to the metric soft conversion.
From [4.6.2.3], the interior strip width is calculated as:
E (interior) = 84 + 1.44 * ( 30 x 39 ) / (12/ft) = 11.1 feet < 12 x 39 / 2 / (12/ft) = 19.5 ft.E (interior) = 11.1 feet
From [4.6.2.1.4b], the edge beam strip width is calculated as:
E (edge) = 1.5 feet (barrier) + 1 foot + x 11.1 feet = 5.275 feet < x 11.1 = 5.55 feet or 6 feet
E (edge) = 5.275 feet
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LRFD Slab Bridge Design, V1.2 Check Page 3 of 34Completed by Kurt Heidenreich, P.E., S.E., KJH Consulting, LLC
DEAD LOAD
The unfactored dead load moments and reactions are provided with the deflection summary table. These
are for slab weight only which is provided below the table. The maximum positive moment in span 2 is18.403 ft-k/ft, and the maximum negative moment at support 2 is 31.597 ft-k/ft. The slab weight is 250
psf which was determined by 150 pcf x 20 / (12/ft).
The future wearing surface load is applied directly to the interior strip unit width (i.e. 35 psf load) for this
case. For the edge beam strip width, the load is only applied to the roadway width. The railing width is
equal to ( 39 36 ) / 2 = 1.5 feet. The edge beam strip load is a ratio of the tributary roadway width ofthe edge beam to the total strip width.
FWS (edge beam) = 35 psf x ( 5.275 ft 1.5 ft ) / ( 5.275 ft ) = 25.05 psf
The railing load is applied to the interior strip and edge beam according to the percentages specified. For
this example 45% was specified for distribution over the bridge width. This results in an equivalent
interior strip load of:
W (interior rail) = 0.45 x 2 x 400 plf / 39 ft = 9.23 psf
The edge beam rail load includes both this distributed portion and 55% of the line load distributed over
the edge beam width.
W (edge beam rail) = 9.23 psf + 0.55 x 400 plf / 5.275ft = 50.94 psf
INTERIOR STRIP CALCULATIONS
For the interior strip design review, the positive moment in span 2 and the negative moment over support2 will be calculated. The design moments are calculated below:
NEGATIVE MOMENT SUPPORT #2 (TOP)
Mu = 31.597 x ( 1.25 + 1.25 x 9.23 / 250 + 1.5 x 35 / 250 ) + 1.75 x 378.96 / 11.1 = 107.336 ft-k
Mu = 1,288,029 in - # / ft width
Mu = 1,287,737 in - # / ft width from report
Ms = 31.597 x ( 1 + 9.23 / 250 + 35 / 250 ) + 378.96 / 11.1 = 71.328 ft-k
Ms = 855,932 in - # / ft width
Ms = 855,766 in - # / ft width from report
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LRFD Slab Bridge Design, V1.2 Check Page 4 of 34Completed by Kurt Heidenreich, P.E., S.E., KJH Consulting, LLC
REQUIRED AREA OF STEEL
d- = 20 2.5 (cover) 0.5 (bar centroid) = 17 inches
Ku = 1,288 in-k / ( 0.9 x 12 x 4 x 172) = 0.1031655
= 0.85 x (1 - ( 1 2.36 x Ku ) ) = 0.110681 = x fc / fy = 0.007379
As = x b x d = 1.505 in2 / ft (1.50 in2 / ft from printout)
FATIGUE STRESS RANGE
Mf (max / min) = -584,250.0 in-#/ft & -430,031.6 in-#/ft
T = C, Fs As = fc b c (c is the depth of the triangular concrete stress block)
Es s As = c Ec b c
c = c s/ ( d c )Es s As = c s Ec b c / ( d c )
As ( d c ) Es / Ec = b c2
n = Es / Ec
Ec = 1,820 fc = 3,640 ksi, Es = 29,000ksin = 29,000 / 3,640 = 7.97
n As d n As c b c2
= 0 b c2 + n As c n As d = 0
A = 0.5 b = 0.5 x 12 = 6
B = n As = 7.97 x 1.505 = 11.995C = - n As d = -7.97 x 1.505 x 17 = -216.8
c = ( -B + ( B2 - 4 A C) ) / ( 2 A )c = 4.915 inches
Tmin = Mfmin / (d c/3) = 430 .0 / ( 17 4.915 / 3 ) = 27.992 kips
fmin = T / As = 27.992 / 1.505 = 18.6 ksi
Tmax = Mfmax / (d c/3) = 584.3 / ( 17 4.915 / 3 ) = 38.036 kips
fmax = T / As = 38.036 / 1.505 = 25.3 ksi
fr = fmax - fmin < 25.3 18.6 = 6.7 ksi < 24 - .33 fmin = 24 - .33 x 18.6 = 17.9 ksi (o.k.)
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LRFD Slab Bridge Design, V1.2 Check Page 5 of 34Completed by Kurt Heidenreich, P.E., S.E., KJH Consulting, LLC
MAXIMUM AREA OF STEEL (STEEL STRAIN)
There is no longer a set maximum area of steel. Instead, the strain at nominal strength is checked to
determine if the section is tension or compression controlled. The steel strain must be greater than 0.005
to be tension controlled and use = 0.9. This is completed in the program by finding the strain for the
maximum moment. If the section isnt tension controlled, the program will require the user to increase
the slab thickness. The strain, in the extreme tension steel, is found by strain compatibility using the fullfactored load at nominal strength.
T = C, As Fy = .85 fc b a, a = As Fy / .85 fc b, c = a /1
s = 0.003 (d c ) / c = 0.003 ( 1 d / a 1) , 1 = 0.85
s = 0.003 ( .85 1 fc b d / As Fy 1)
s = 0.003 ( .85 x .85 x 4 x 12 x 17 / ( 1.505 x 60 ) 1) = 0.01659 > 0.005 (Tension Controlled)
MINIMUM AREA OF STEEL
For the minimum steel requirement, the provided steel must be greater than that required to meet 1.2Mcr,
or at least 1.33 times the calculated steel if it is less than 1.2Mcr.
Fr = 0.37 fc = 0.74 ksiS = b t2 / 6 = 12 x 202 / 6 = 800 in3
1.2Mcr = 1.2 Mcr S = 1.2 x 0.74 x 800 = 710.4 in-k/ft < Mu = 1,288 in-k/ft (o.k.)
CRACK CONTROL MAXIMUM SPACING
For crack control the modulus of rupture is lower per [5.4.2.6]. If the service moment is greater than 80%
of the cracking moment, the maximum spacing in [5.7.3.4] must be checked.
From report, Bar 1 is a #9 bar and Bar 2 is a #7 bar at a spacing of 6 inches
As (provided) = 1.60 in2
/ ft
Fr = 0.24 fc = 0.48 ksi
0.8Mcr = 0.8 Mcr S = 0.8 x 0.48 x 800 = 307.2 in-k/ft < Ms = 856 in-k/ft
S < 700 e /s fss 2 dc
s = 1 + dc / 0.7 ( h - dc )
e = 0.75
Average Bar Diameter = ( 0.875 + 1.128 ) / 2 = 1.0015
dc = 2.5 (top cover) + 1.0015 / 2 = 3.0
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LRFD Slab Bridge Design, V1.2 Check Page 6 of 34Completed by Kurt Heidenreich, P.E., S.E., KJH Consulting, LLC
s = 1 + 3 / 0.7 ( 20 - 3 ) = 1.252
A = 0.5 b = 0.5 x 12 = 6
B = n As = 7.97 x 1.6 = 12.752
C = - n As d = -7.97 x 1.6 x 17 = -216.8
c = 5.04 inches (see page 4 for c calculation details)
T = Ms / (d c/3) = 856 / ( 17 5.04 / 3 ) = 55.875 kipsFss = T / As = 55.875 / 1.6 = 34.922 ksi
S < 700 x .75 / ( 1.252 x 34.922ksi ) 2 x 3 = 6.01 inches (6.01 from report)
POSITIVE MOMENT SPAN #2 (BOTTOM)
Mu = 1.25 M(slab) + 1.25 M(rail) + 1.5 M(fws) + 1.75 M(live) / EMu = 18.403 x ( 1.25 + 1.25 x 9.23 / 250 + 1.5 x 35 / 250 ) + 1.75 x 452.38 / 11.1 = 99.039ft-kMu = 1,188,466 in - # / ft width
Mu = 1,188,102.0 in-#/ft from report
Ms = 18.403 x ( 1 + 9.23 / 250 + 35 / 250 ) + 452.38 / 11.1 = 62.414ft-k
Ms = 748,966 in - # / ft width
Ms = 748,757 in-#/ft from report
REQUIRED AREA OF STEEL
d+ = 20 1 (cover) 1 (tire wear) 0.5 (bar centroid) = 17.5 inches
b = 12, fc = 4ksi, fy = 60ksi
Ku = Mu / ( x b x fc x d2
)
Ku = 1,188 in-k / ( 0.9 x 12 x 4 x 17.52) = 0.089796
= 0.85 x (1 - ( 1 2.36 x Ku ) ) = 0.09542132 = x fc / fy = 0.0063614
As = x b x d = 1.336 In2
/ ft (1.34 from program)
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LRFD Slab Bridge Design, V1.2 Check Page 7 of 34Completed by Kurt Heidenreich, P.E., S.E., KJH Consulting, LLC
FATIGUE STRESS RANGE
Check the calculated area of steel for the fatigue stress range.
Mf (max / min) = 239,631 in-#/ft & 385,863 in-#/ft
A = 0.5 b = 0.5 x 12 = 6B = n As = 7.97 x 1.336 = 10.648C = - n As d = -7.97 x 1.336 x 17 = -186.339
c = 4.755 inches (see page 4 for c calculation details)
Tmin = 239.6 / ( 17.5 4.755 / 3 ) = 15.055 kips
fmin = 15.055 / 1.336 = 11.3 ksi
Tmax = 385.9 / ( 17.5 4.755 / 3 ) = 24.248 kips
fmax = 24.248 / 1.336 = 18.2 ksi
fr = fmax - fmin < 18.2 11.3 = 6.9 ksi < 24 - .33 x 11.3 = 20.3 ksi (o.k.)
MAXIMUM AREA OF STEEL (STEEL STRAIN)
s = 0.003 ( .85 x .85 x 4 x 12 x 17.5 / ( 1.336 x 60 ) 1) = 0.01971 > 0.005 (Tension Controlled)
MINIMUM AREA OF STEEL
1.2Mcr = 710.4 in-k/ft < Mu = 1,188 in-k/ft (o.k.)
CRACK CONTROL MAXIMUM SPACING
From report, Bar 1 is a #8 bar and Bar 2 is a #7 bar at a spacing of 6 inches
As (provided) = 1.39 in2
/ ft
0.8Mcr = 0.8 Mcr S = 0.8 x 0.48 x 800 = 307.2 in-k/ft < Ms = 749 in-k/ft
e = 0.75
Average Bar Diameter = ( 0.875 + 1) / 2 = 0.9375dc = 1 (lower cover) + 0.9375 / 2 = 1.47
s = 1 + 1.47 / 0.7 ( 20 1.47 ) = 1.113
A = 0.5 b = 0.5 x 12 = 6
B = n As = 7.97 x 1.39 = 11.078C = - n As d = -7.97 x 1.39 x 17.5 = -193.87
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c = 4.835 inches (see page 4 for c calculation details)
T = Ms / (d c/3) = 749 / ( 17.5 4.835 / 3 ) = 47.142 kips
Fss = T / As = 47.142 / 1.39 = 33.915 ksi
S < 700 x .75 / ( 1.113 x 33.915 ksi ) 2 x 1.47 = 10.97 inches (11.0 from report)
NEGATIVE MOMENT SUPPORT #2 (BAR CUTOFF)
The top steel bar cutoff for support 2 in span 1 will be used for this example. Bar 2 is cut at the location
where Bar 1 area of steel at twice the spacing equals the required steel.
Bar 1 is a #9 bar and Bar 2 is a #7 bar at a spacing of 6 inches
As (Bar 1 @ 12) = 1.0 in2
/ ft
As (reqd) = 0.8 in2 / ft 24 feet
As (reqd) = 1.01 in2
/ ft 27 feet
Theoretical Cutoff = 24 + (27 - 24) x (1.0 - 0.8) / (1.01 - 0.8) = 26.857 Feet
The bar must be extended the greater of: d(neg), 15db, or Span/20
Span / 20 = 30 / 20 = 1.5 (controls)
Bar 2 theoretically begins at 26.857 1.5 = 25.357
MLL = -222.507 Ft-k, MSLAB = 1.507 Ft-k @ 21
MLL = -254.293 Ft-k, MSLAB = -7.278 Ft-k @ 24MLL = -294.343 Ft-k, MSLAB = -18.313 Ft-k @ 27
Ms @ 21 = 1.507 x ( 1 + 9.23 / 250 + 35 / 250 ) 222.507 / 11.1 = -18.272 ft-kMs @ 21 = 219,265 in - # / ft width
Ms @ 24 = -7.278 x ( 1 + 9.23 / 250 + 35 / 250 ) 254.293 / 11.1 = -31.475 ft-kMs @ 24 = 377,699 in - # / ft width
Ms @ 27 = -18.313 x ( 1 + 9.23 / 250 + 35 / 250 ) 294.343 / 11.1 = -48.070 ft-k
Ms @ 27 = 576,844 in - # / ft width
Ms @ 25.357 = 377,699 + (576,844 - 377,699) x (25.357 - 24) / (27 - 24) = 467,779 in - #
dc = 2.5 (top cover) + 1.128 / 2 = 3.064
s = 1 + 3.064 / 0.7 ( 20 3.064 ) = 1.258
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A = 0.5 b = 0.5 x 12 = 6B = n As = 7.97 x 1.0 = 7.97
C = - n As d = -7.97 x 1.0 x 17.5 = -139.475
c = 4.203 inches (see page 4 for c calculation details)
T = Ms / (d c/3) = 468 / ( 17 4.203 / 3 ) = 30.00 kipsFss = T / As = 30.00 / 1.0 = 30.00 ksi
S < 700 x .75 / ( 1.258 x 30.00 ) 2 x 3.064 = 7.78 inches
Since the spacing of bar 1 is 12 inches beyond the cutoff, and this exceeds the 7.78 maximum
spacing, no cutoff is allowed at this point. The program iterated until a suitable cutoff was found
at 23.60 feet. Check this cutoff point for spacing requirements.
Ms @ 23.60 = 219,265 + (377,699 - 219,265) x (23.60 - 21) / (24 - 21) = 356,575 in - #
T = Ms / (d c/3) = 356.6 / ( 17 4.203 / 3 ) = 22.86 kipsFss = T / As = 22.86 / 1.0 = 22.86 ksi
S < 700 x .75 / ( 1.258 x 22.86 ) 2 x 3.064 = 12.13 inches (12.10 from report)
For strength purposes, Bar 1 must be developed from the theoretical cutoff point of Bar 2 at 26.857 feet.
The basic development length is calculated in accordance with [5.11.2.1]
Ldb = 1.25 Ab Fy /Fc = 1.25 x 1.0 x 60 /4 = 37.5 inches
The modification factor for top reinforcing and epoxy coating has a maximum value of 1.7, which is used
here.
Ld = 37.5 x 1.7 / (12/ft) = 5.3125 feet
Bar 1 must extend at least to 26.857 5.3125 = 21.55 feet
This program provides the cutoff for Bar 1 at the inflection point. If there isnt an inflection point, thetheoretical location where a temperature and shrinkage bar meets the required area of steel is provided. In
that case, the designer must decide where to cut or splice reinforcing bars.
For this example, the first point with a required area of steel equal to zero is at the 4/10th point, or at a
distance of 12.0 feet. The bar extension for inflection point cuts is: d, 12db or 0.0625 x Span.
0.0625 x Span = 0.0625 x 30 = 1.875 (controls)
Bar 1 begins at 12.0 1.875 = 10.125 (10.13 from report)
Since this is well beyond the development length for the Bar 2 cut and since there isnt any negative
moment at this point to require a crack control check, this is a valid cutoff point for Bar 1. Temperature
and shrinkage reinforcing should be spliced at each Bar 1 cutoff according to the report printout.
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LRFD Slab Bridge Design, V1.2 Check Page 10 of 34Completed by Kurt Heidenreich, P.E., S.E., KJH Consulting, LLC
POSITIVE MOMENT SPAN #2 (BAR CUTOFF)
The cutoff location for Bar 2 bottom steel in span 2 will be calculated. Bar 1 is continuous to meet code
requirements. Bar 2 is cut at the location where Bar 1 area of steel at twice the spacing equals the
required steel.
Bar 1 is a #8 bar and Bar 2 is a #7 bar at a spacing of 6 inches
As (Bar 1 @ 12) = 0.79 in2 / ft
As (reqd) = 0.65 in2
/ ft 8 feetAs (reqd) = 0.95 in2 / ft 12 feet
Theoretical Cutoff = 8 + (12 - 8) x (0.79 - 0.65) / (0.95 - 0.65) = 9.87 Feet
The bar must be extended the greater of: d(pos), 15db, or Span/20
Span / 20 = 40 / 20 = 2.0 (controls)
Bar 2 theoretically begins at 9.87 2.0 = 7.87
MLL = 90.095 Ft-k, MSLAB = -13.597 Ft-k @ 4MLL = 232.592 Ft-k, MSLAB = 0.403 Ft-k @ 8
Ms @ 4 = -13.597 x ( 1 + 9.23 / 250 + 35 / 250 ) + 90.095 / 11.1 = -7.89 ft-kMs @ 4 = -94,631 in - # / ft width
Ms @ 8 = 0.403 x ( 1 + 9.23 / 250 + 35 / 250 ) + 232.592 / 11.1 = 21.43 ft-k
Ms @ 8 = 257,142 in - # / ft width
Ms @ 7.87 = -94,631 + (257,142 - -94,631) x (7.87 - 4) / (8 - 4)
Ms @ 7.87 = 245,709 in - #/ft (246880 in - # from report)Ms @ 7.87 < 0.8Mcr = 307,200 in-#/ft
Spacing check is not required. Use the cutoff at 7.87 (7.88 from report)
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EDGE BEAM STRIP CALCULATIONS
The edge beam strip design follows the same methodology as the interior strip. The live load is applied as
of the lane, and the dead load is that portion discussed in the dead load section. The same bars are usedas determined for the interior strip. If the calculated edge beam spacing is larger than the interior strip,
the same spacing as the interior strip must be used. If the edge beam spacing is less than the interior strip,
the bar spacing must adjusted accordingly for the edge beam width to be less than the calculated value.
If the edge beam spacing is less than the interior strip, it is likely the bar cutoffs will be longer for the
edge beam steel. Different bars can be provided in the edge beam width, or the longer bars can be used inthe interior strip and edge beam at the designers discretion.
While superstructure shear design calculations are not required by the code [5.14.4.1] since the moment
design is in accordance with [4.6.2.3], designers may want to see the calculated shear loads for the interiorand edge beam strips. The shear summary table is printed if the designer checks the appropriate box on
the loading page.
SUPPORT #1 DESIGN
Support #1 is an integral cap type which is assumed to behave as a flexural member. A pavement load of
1 klf is applied. Dynamic load allowance is not applied for piling design.
Puwheel (w/ dynamic) = 1.75 x 1.33 x 16 kips = 37.24 kips
Puwheel (w/o dynamic) = 1.75 x 16 kips = 28 kips
RuLL (w/ dynamic) = 1.75 x 70.89 kips = 124.06 kips
wuLL (w/ dynamic) = 2 lanes x ( 124.06 k 37.24 k x 2 wheels ) / 39 feet = 2.54 klf
RuLL (w/o dynamic) = 97.10 kipswuLL (w/o dynamic) = 2 lanes x ( 97.10 k 28 k x 2 wheels ) / 39 feet = 2.108 klf
wucap = 1.25 x 0.15 x ( tslab x bottom width /2* + cap drop x bottom width ) / (12/ft x 12/ft)* This includes the weight of concrete on the pavement ledge
wucap = 1.25 x 0.15 x ( 20 x 30/2 + 18 x 30 ) / 144 = 1.094 klf
wuslab = 1.25 x Rslab = 1.25 x 2.7 klf = 3.375 klf
wufws = 1.5 x ( 35 psf x 36 / 39 ) / 250 psf x 2.7 klf = 0.523 klf
wurail = ( 0.45 x 2 rails x 400plf / 39 ) / 250 psf x 3.375 klf = 0.125 klf
wu = 1.25 x wpavement + wucap + wuslab + wufws + wurail + wuLL
wu (w/ dynamic) = 1.25 x 1 + 1.094 + 3.375 + 0.523 + 0.125 + 2.54 = 8.91 klf
wu (w/o dynamic) = 1.25 x 1 + 1.094 + 3.375 + 0.523 + 0.125 + 2.108 = 8.48 klf
wurail (edge beam) = ( 0.55 x 400plf / 5.28 ) / 250 psf x 3.375 klf = 0.5625 klf
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There are 6 - piles spaced at 6-6 on center. This results in a cap overhang of ( 39 5 x 6.5 ) / 2 = 3.25
feet which matches the report calculation.
EXTERIOR PILING DESIGN
The exterior pile load is calculated by the lever rule assuming a pin at the first interior pile. The firstwheel load is placed at 1 foot from the rail in accordance with the code. The rail width is 1.5 feet so the
distance from the outside of bridge to the first wheel load is 2.5 feet and the distance from the first pile to
the outside of bridge is 6.5+3.25 = 9.75 feet. Since the next wheel load, at 6 feet away from the first, isat 8.5 feet from the outside edge of the bridge, it also contributes to the exterior pile load. The exterior
piling load is calculated as follows:
Puext = { 8.48klf x 9.75 x 9.75 /2 + 0.5625 x 5.28 x ( 9.75 - 5.28/2 ) + 28k x ( 9.75 - 2.5 ) +
28k x ( 9.75 8.5 ) } / 6.5 = 101.87 kips (101.79 k from report)
INTERIOR PILING DESIGN
The interior pile load is calculated assuming a two span condition for point loads. The equations, in theAISC manual, for a two equal span condition with a concentrated load at any point was used. The spans
are broken into 1/10th
points and the wheel loads are all placed at each tenth point to determine the
maximum reaction. Since this bridge has two lanes, there are four wheels to check at 6, 4, 6 spacingbetween loads. The maximum pile load for this case occurs when the one wheel is at the 7/10th point and
a second wheel is 4 feet ahead of it in the second span. Using the two span reaction formula, this
condition produces a maximum wheel load reaction of 48.86 kips.
a = 0.7 x 6.5 = 4.55 feet
a = 2 x 6.5 ( 4.55 + 4 ) = 4.45 feet (span 2 contribution, reverse dimension)
R2 = 28k x 4.55 x ( 2 x 6.52 + (6.5 4.55) x (6.5 + 4.55) ) / (2 x 6.53) +
28k x 4.45 x ( 2 x 6.52
+ (6.5 4.45) x (6.5 + 4.45) ) / (2 x 6.53)
R2 = 48.86 kips
The distributed load is applied by tributary area by multiplying it by the pile spacing. The interior piling
load is calculated as follows:
Puint = 8.48klf x 6.5 + 48.86 k = 103.98 kips (103.91 k from report)
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UPLIFT PILING DESIGN
To determine if the structure has ample dead load to resist negative live load reactions, an uplift check is
complete.
RuLL (w/ dynamic) = 2 lanes x -14.76 kips = -29.52 kips
wcap = 0.9 x 0.15 x ( 20 x 30/2 + 18 x 30 ) / 144 = 0.788 klf
wslab = 0.9 x 2.7 klf = 2.43 klf
wfws may not be placed so it is not included
wrail = 0.9 x ( 2 rails x 400plf / 39 ) / 250 psf x 2.7 klf = 0.20 klf
Rmin = ( 0.9 x wpavement + wucap + wuslab + wurail ) x 39 + wuLL
Rmin = ( 0.9 x 1 + .788 + 2.43 + 0.20 ) x 39 29.52 = 138.88 k (138.71 k from report)
Rmin = 138.88 k / 6 piles = 23.15 k / pile (23.12 k / pile from report)
FLEXURAL DESIGN
Flexural design includes three moment calculations: Mucant (the cantilevered portion of the overhang),
Muneg (negative moment over an interior pile), Mupos (the positive moment between two interior piles). Ifthere are only two piles, the negative moment equals the cantilevered moment, and the analysis is based
on a simple span. If there are more than two piles, the program uses a two span condition, similar to the
pile calculations, to conservatively find the positive and negative moments. Using the loads calculated in
the piling section with dynamic load allowance included:
Mucant = ( wu (w/ dynamic) + wurail (edge beam) ) x 3.252/2 + Puwheel (w/ dynamic) x ( 3.25 2.5)
Mucant = ( 8.91klf + 0.5625klf ) x 3.252
/2 + 37.24 x ( 3.25 2.5 ) = 77.96kMucant = 935,479.7 in-# (935,105.7 in-# from report)
d- = 32 inchesb = 30 inches
Ku = 935.5 in-k / ( 0.9 x 30 x 4 x 322) = 0.00846
= 0.85 x (1 - ( 1 2.36 x Ku ) ) = 0.00853 = x fc / fy = 0.0005687
As = x b x d = 0.546 In2 (0.55 In2 from report)
The minimum steel check is based on the depth of slab plus the cap drop for the specified design width.
This value must be verified by the designer.
S = b t2 / 6 = 30 x (20+18)2 / 6 = 7,220 in3
1.2Mcr = 1.2 Mcr S = 1.2 x 0.74 x 7,220 = 6,411.4 in-k
Ku = 6,411.4 in-k / ( 0.9 x 30 x 4 x 322) = 0.05797
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LRFD Slab Bridge Design, V1.2 Check Page 14 of 34Completed by Kurt Heidenreich, P.E., S.E., KJH Consulting, LLC
= 0.85 x (1 - ( 1 2.36 x Ku ) ) = 0.06029 = x fc / fy = 0.00402
As = x b x d = 3.86 In2 (3.85 In2 from report)
For the interior negative moment, the maximum value occurs at the 7/10th
point with one wheel load 6
feet ahead in span 2 and one behind at 4 feet. The distributed load is included as 0.1wL
2
.
a = 0.7 x 6.5 = 4.55 feet
a = 4.55 4 = 0.55 feet (span 1)a = 2 x 6.5 ( 4.55 + 6 ) = 2.45 feet (span 2 contribution, reverse dimension)
Muneg = 37.24k x 4.55 x (6.5 4.55) x (6.5 + 4.55) / (4 x 6.52) +
37.24k x 0.55 x (6.5 0.55) x (6.5 + 0.55) / (4 x 6.52) +
37.24k x 2.45 x ( (6.5 2.45) x (6.5 + 2.45) ) / (4 x 6.52) +
0.1 x 8.91klf x 6.52
= 83.91 k
Muneg = 1,006,857 in-# (1,006,531 in-# from report)
d- = 32 inchesb = 30 inches
Ku = 1,006.9 in-k / ( 0.9 x 30 x 4 x 322) = 0.00911
= 0.85 x (1 - ( 1 2.36 x Ku ) ) = 0.00918 = x fc / fy = 0.000612
As = x b x d = 0.588 In2 (0.59 In2 from report)
For the interior positive moment, the maximum value occurs at the 4/10th
point. No other wheel loads
contribute. The distributed load is included as 0.1wL2.
a = 0.4 x 6.5 = 2.6 feet
Mupos = 37.24k x 2.6 x (6.5 2.6 ) x (4 x 6.52 2.6 x (6.5 + 2.6) / (4 x 6.53) + 12.81
0.1 x 8.91klf x 6.52 = 83.91 k87.604
Mupos = 1,051,245 in-# (1,050,986 in-# from report)
d- = 33 inches
b = 24 inchesKu = 1,051.3 in-k / ( 0.9 x 24 x 4 x 332) = 0.0112
= 0.85 x (1 - ( 1 2.36 x Ku ) ) = 0.0113 = x fc / fy = 0.000753
As = x b x d = 0.597 In2 / ft (0.60 In2 from report)
S = b t2 / 6 = 24 x (20+18)2 / 6 = 5,776 in3
1.2Mcr = 1.2 Mcr S = 1.2 x 0.74 x 5,776 = 5,129.1 in-k
Ku = 5,129.1 in-k / ( 0.9 x 24 x 4 x 332) = 0.0545
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LRFD Slab Bridge Design, V1.2 Check Page 15 of 34Completed by Kurt Heidenreich, P.E., S.E., KJH Consulting, LLC
= 0.85 x (1 - ( 1 2.36 x Ku ) ) = 0.0566 = x fc / fy = 0.00377
As = x b x d = 2.99 In2 (2.98 In2 from report)
SHEAR DESIGN
Shear design includes two calculated values: Vucant (the cantilevered portion of the overhang), Vuint
(interior shear close to a pile). If there are only two piles, the analysis is based on a simple span for theinterior condition. If there are more than two piles, the program uses the two span condition similar to the
other design checks. Using the loads calculated in the piling section with dynamic load allowance
included:
Vucant = ( wu (w/ dynamic) + wurail (edge beam) ) x 3.25 + Puwheel (w/ dynamic)
Vucant = ( 8.91klf + 0.5625klf ) x 3.25 + 37.24k = 68.03 k (68.01 k from report)
For the interior shear, the maximum value occurs with a load at the end of the first span. Another wheel
load is 4 behind in span 1 and a third is 6 ahead in span 2. The distributed load is included as 5/8wL.
a = 6.5 feet
a = 6.5 4 = 2.5 feet (span 1)
a = 6.5 6 = 0.5 feet (span 2 contribution, reverse dimension use V3)
Vuint = 5/8 x 8.91klf x 6.5 + 37.24k +
37.24k x 2.5 x ( 4 x 6.52
+ (6.5 2.5) x (6.5 + 2.5) ) / (4 x 6.53) +
37.24k x 0.5 x ( 6.5 0.5) x (6.5 + 0.5) ) / (4 x 6.53)
Vuint = 91.52 k (91.50 k from report)
Shear design is based on the simplified method [5.8.3.3 using 5.8.3.4.1] with Beta = 2.0 for concretestrength calculations. The calculated shear steel area is provided in square inches per foot for both stirrup
legs. If this method is used, the minimum shear steel must be provided as calculated. The designer can
perform more detailed shear calculations using the shear forces provided if this method does not producedesired results.
Vc = x 0.0316 x x fc x bv x dv = 0.9
= 2.0
bv = 24 inches
dv = 20 inches
Vc = 0.9 x 0.0316 x 2.0 x 4 x 24 x 20 = 54.6k (54.60 kips form report)
If Vu > Vc then shear steel is calculated.
Vs = x Av x Fy x dv / s
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Vu = Vc +Vs
Vu - Vc = Vs = x Av x Fy x dv / s
Av / s = ( Vu - Vc ) / x Fy x dv
Av / s = ( 91.52 - 54.6 ) / 0.9 x 60 x 20 = 0.03419 In2
/ inAv / s = 0.41 In
2 / ft (0.41 In2 / ft from report)
Minimum shear reinforcing is required if Vu > Vc/2. The minimum shear steel is calculated according
to the following equation.
Av = 0.0316 x fc x bv x s / FyAv / s = 0.0316 x 4 x 24 / 60 = 0.02528 In2 / inAv / s = 0.303 In
2/ ft (0.30 In
2/ ft. from report)
Therefore, the calculated shear reinforcement area of 0.41 In2 / ft. controls. This is approximately a #4
stirrup at 12 inches on center.
Av = 2 x 0.2 In2 / 1.0 ft spacing = 0.40 In2 / ft.
Most standard details for integral slab type substructures provide minimum reinforcing for shear and
flexure that exceed calculated requirements for typical conditions.
SUPPORT #2 DESIGN
Support #2 is a wall type substructure which is assumed to behave as a rigid member. Because it is an
interior condition, there is no pavement load. Dynamic load allowance is not applied for piling design.
RuLL (w/o dynamic) = 158.53 kips
Rucap = 1.25 x 0.15 x ( 24/12 ) x ( 144/12 ) x 39 = 175.5 k
Ruslab = 1.25 x 39 x Rslab = 1.25 x 39 x 9.8 klf = 477.75 k
Rufws = 1.5 x 36 x ( 35 psf / 250psf ) x 9.8 klf = 74.09 k
Rurail = 1.25 x 2 rails x 400plf / 250 psf x 9.8 klf = 39.2 k
RuD = 175.5 + 477.5 + 74.09 + 39.2 = 766.29 k
There are 7 - piles spaced at 6-0 on center. This results in a cap overhang of ( 39 6 x 6.0 ) / 2 = 1.5
feet which matches the report calculation.
N = 7
Ip = 2 x ( 62
+ 122
+ 182
) = 1,008 ft2
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LRFD Slab Bridge Design, V1.2 Check Page 17 of 34Completed by Kurt Heidenreich, P.E., S.E., KJH Consulting, LLC
yext = 18 feetSext = Ip / yext = 1,008 ft
2 / 18 = 56 ft.
PD = RuD / N = 766.29 k / 7 = 109.47 k
Each lane is assumed to occupy a 10 width. The exterior pile loads are provided as the maximum and
minimum values.
PL = RuL / N + e x RuL / S
e1 = 39 / 2 - 1.5 (rail) 10 / 2 = 13e2 = 13 10 = 3
Find maximum exterior pile load
P1max = 158.53 k / 7 + 13 x 158.53 k / 56 = 59.45 k
P1min = 158.53 k / 7 - 13 x 158.53 k / 56 = -14.16 k
P2max = 158.53 k / 7 + 3 x 158.53 k / 56 = 31.14 k
P2min = 158.53 k / 7 - 3 x 158.53 k / 56 = 14.15 k
Pmax = 109.47 + 41.05 + 26.89 = 200.06 k ( 200.12 k from report )
Since the second lane load would increase the pile load, it is neglectedPmin = 109.47 -14.16 = 95.31 k ( 95.38 k from report )
UPLIFT PILING DESIGN
RuLL (w/ dynamic) = 2 lanes x -12.02 kips = -24.04 kips
wcap = 0.9 x 0.15 x 24 x 144 / 144 = 3.24 klf
wslab = 0.9 x 9.8 klf = 8.82 klf
wfws may not be placed so it is not included
wrail = 0.9 x ( 2 rails x 400plf / 39 ) / 250 psf x 9.8 klf = 0.724 klf
Rmin = ( wucap + wuslab + wurail ) x 39 + wuLL
Rmin = ( 3.24 + 8.82 + 0.724 ) x 39 24.04 = 474.54 k (474.65 k from report)Rmin = 474.54 k / 7 piles = 67.79 k / pile (67.81 k / pile from report)
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OUPUT FILE
REPORT
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******************************************************************************
******** CAST IN PLACE REINFORCED CONCRETE SLAB BRIDGE DESIGN PROGRAM ********
******** Copyright (C) KJH Consulting, LLC, 2008. All Rights Reserved. *******
******** KJH Consulting, LLC ******************************* Page____of____ **
******************************************************************************
JOB DESCRIPTION: Example Project
------------------------------------------------------------------------------
THE BRIDGE IS A 3 SPAN CONTINUOUS SLAB
SLAB DEPTH REQUIRED (S + 10) / 30 = 20.00 In.
SLAB DEPTH PROVIDED = 20.00 In.
SPAN # 1 LENGTH OF SPAN = 30.00 Ft.
SPAN # 2 LENGTH OF SPAN = 40.00 Ft.
SPAN # 3 LENGTH OF SPAN = 30.00 Ft.
-------------------------------{ GEOMETRICS }---------------------------------
ROADWAY WIDTH = 36.00 ft.
OUT TO OUT BRIDGE WIDTH = 39.00 ft.
NUMBER OF TRAFFIC LANES = 2
UPPER CLEAR COVER = 2.50 In.
LOWER CLEAR COVER = 1.00 In.
TIRE WEAR DEPTH = 1.00 In.
BRIDGE SKEW = 0.00 Deg.
MOMENT DESIGN SKEW FACTOR = 1.000
TOP EXPOSURE FACTOR = 0.750
BOTTOM EXPOSURE FACTOR = 0.750
--------------------------{ MATERIAL PROPERTIES }----------------------------
Fy = 60.00 ksiF'c = 4.00 ksi
TOP REINFORCING IS EPOXY COATED
--------------------------{ APPLIED LOAD SUMMARY }----------------------------
RAILING LOAD / SIDE = 400.00 plf
45% RAILING LOAD TO BRIDGE & 55% TO EDGE BEAM
FUTURE WEARING SURFACE = 35.00 psf
FATIGUE WIDTH = 1.2 x SINGLE LANE DISTR. = 16.00 ft./Lane
INTERIOR DISTRIBUTION WIDTH = 11.10 ft./Lane
EDGE BEAM WIDTH = 5.28 ft./Side
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******************************************************************************
******** CAST IN PLACE REINFORCED CONCRETE SLAB BRIDGE DESIGN PROGRAM ********
******** Copyright (C) KJH Consulting, LLC, 2008. All Rights Reserved. *******
******** KJH Consulting, LLC ******************************* Page____of____ **
********************* SINGLE TRUCK WITH LANE LOADING *************************
S U M M A R Y T A B L E
Includes 1.33 Impact Factor on Truck Load______________________________________________________________________________
_______MOMENTS_______ _______SHEAR________ _____REACTIONS_____
LOCATION POSITIVE NEGATIVE POSITIVE NEGATIVE MAXIMUM MINIMUM
(FT) (FT-K/LANE) (FT-K/LANE) (K/LANE) (K/LANE) (K/LANE) (K/LANE)
------------------------------------------------------------------------------
Support # 1 70.89 -10.60
0.00 0.000 0.000 70.890 -10.596
3.00 179.460 -31.787 58.978 -10.714
6.00 297.440 -63.573 48.125 -17.287
9.00 358.588 -95.360 38.020 -23.795
12.00 368.982 -127.147 28.774 -29.925
15.00 342.902 -158.933 20.062 -35.593
18.00 337.370 -190.720 14.608 -42.64421.00 281.063 -222.507 10.115 -53.601
24.00 177.577 -254.293 6.211 -64.058
27.00 81.645 -294.343 2.933 -73.843
30.00 59.310 -378.961 74.502 -82.880
Support # 2 111.74 -8.65
0.00 59.310 -378.961 88.062 -71.344
4.00 74.503 -209.615 76.472 -6.759
8.00 206.842 -154.569 64.324 -7.743
12.00 337.588 -130.877 52.394 -15.302
16.00 412.265 -108.507 40.475 -22.502
20.00 425.778 -86.138 29.983 -29.983
24.00 412.265 -108.507 22.502 -40.475
28.00 337.588 -130.877 15.302 -52.394
32.00 206.842 -154.569 7.743 -64.32436.00 74.503 -209.615 6.759 -76.472
40.00 59.310 -378.961 71.344 -88.062
Support # 3 111.74 -8.65
0.00 59.310 -378.961 82.880 -74.502
3.00 81.645 -294.343 73.843 -2.933
6.00 177.576 -254.294 64.058 -6.211
9.00 281.063 -222.507 53.601 -10.115
12.00 337.370 -190.720 42.644 -14.608
15.00 342.902 -158.933 35.593 -20.062
18.00 368.982 -127.147 29.925 -28.774
21.00 358.588 -95.360 23.795 -38.020
24.00 297.440 -63.573 17.287 -48.125
27.00 179.460 -31.787 10.714 -58.97830.00 0.000 0.000 10.596 -70.890
Support # 4 70.89 -10.60
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******************************************************************************
******** CAST IN PLACE REINFORCED CONCRETE SLAB BRIDGE DESIGN PROGRAM ********
******** Copyright (C) KJH Consulting, LLC, 2008. All Rights Reserved. *******
******** KJH Consulting, LLC ******************************* Page____of____ **
************************ TANDEM WITH LANE LOADING ****************************
S U M M A R Y T A B L E
Includes 1.33 Impact Factor on Tandem Load______________________________________________________________________________
_______MOMENTS_______ _______SHEAR________ _____REACTIONS_____
LOCATION POSITIVE NEGATIVE POSITIVE NEGATIVE MAXIMUM MINIMUM
(FT) (FT-K/LANE) (FT-K/LANE) (K/LANE) (K/LANE) (K/LANE) (K/LANE)
------------------------------------------------------------------------------
Support # 1 69.86 -9.72
0.00 0.000 0.000 69.858 -9.717
3.00 182.369 -29.150 59.948 -9.835
6.00 311.257 -58.300 50.428 -13.236
9.00 388.899 -87.450 41.388 -21.837
12.00 418.647 -116.600 32.913 -30.444
15.00 411.951 -145.750 25.088 -38.956
18.00 376.141 -174.901 17.993 -47.26821.00 302.491 -204.051 11.708 -55.271
24.00 197.705 -233.201 6.307 -62.856
27.00 77.866 -270.613 2.038 -69.908
30.00 59.475 -325.101 64.453 -76.312
Support # 2 92.60 -8.67
0.00 59.475 -325.101 78.013 -64.776
4.00 90.095 -197.506 70.166 -6.777
8.00 232.592 -154.998 61.410 -9.202
12.00 355.786 -131.231 52.107 -16.237
16.00 431.404 -108.788 42.606 -24.352
20.00 452.378 -86.344 33.247 -33.247
24.00 431.404 -108.788 24.352 -42.606
28.00 355.786 -131.231 16.237 -52.107
32.00 232.592 -154.998 9.202 -61.41036.00 90.095 -197.506 6.777 -70.166
40.00 59.475 -325.101 64.776 -78.013
Support # 3 92.60 -8.67
0.00 59.475 -325.101 76.312 -64.453
3.00 77.866 -270.613 69.908 -2.038
6.00 197.705 -233.201 62.856 -6.307
9.00 302.491 -204.051 55.271 -11.708
12.00 376.141 -174.901 47.268 -17.993
15.00 411.951 -145.751 38.956 -25.088
18.00 418.647 -116.600 30.444 -32.913
21.00 388.899 -87.450 21.837 -41.388
24.00 311.257 -58.300 13.236 -50.428
27.00 182.369 -29.150 9.835 -59.94830.00 0.000 0.000 9.717 -69.858
Support # 4 69.86 -9.72
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******************************************************************************
******** CAST IN PLACE REINFORCED CONCRETE SLAB BRIDGE DESIGN PROGRAM ********
******** Copyright (C) KJH Consulting, LLC, 2008. All Rights Reserved. *******
******** KJH Consulting, LLC ******************************* Page____of____ **
********************** TWIN TRUCKS WITH LANE LOADING *************************
S U M M A R Y T A B L E
90% of Twin Trucks (with 1.33 Impact Factor) + 90% of Lane Load______________________________________________________________________________
_______MOMENTS_______ _______SHEAR________ _____REACTIONS_____
LOCATION POSITIVE NEGATIVE POSITIVE NEGATIVE MAXIMUM MINIMUM
(FT) (FT-K/LANE) (FT-K/LANE) (K/LANE) (K/LANE) (K/LANE) (K/LANE)
------------------------------------------------------------------------------
Support # 1 0.00 0.00
0.00 0.000 0.000 0.000 0.000
3.00 0.000 -28.608 0.000 0.000
6.00 0.000 -57.216 0.000 0.000
9.00 0.000 -85.824 0.000 0.000
12.00 0.000 -114.432 0.000 0.000
15.00 0.000 -143.040 0.000 0.000
18.00 0.000 -171.648 0.000 0.00021.00 0.000 -200.256 0.000 0.000
24.00 0.000 -228.864 0.000 0.000
27.00 0.000 -264.908 0.000 0.000
30.00 0.000 -329.650 0.000 0.000
Support # 2 100.56 0.00
0.00 0.000 -329.650 0.000 0.000
4.00 0.000 -177.303 0.000 0.000
8.00 0.000 -139.112 0.000 0.000
12.00 0.000 -128.293 0.000 0.000
16.00 0.000 -122.493 0.000 0.000
20.00 0.000 -117.552 0.000 0.000
24.00 0.000 -122.493 0.000 0.000
28.00 0.000 -128.293 0.000 0.000
32.00 0.000 -139.112 0.000 0.00036.00 0.000 -177.303 0.000 0.000
40.00 0.000 -329.650 0.000 0.000
Support # 3 100.56 0.00
0.00 0.000 -329.650 0.000 0.000
3.00 0.000 -264.908 0.000 0.000
6.00 0.000 -228.864 0.000 0.000
9.00 0.000 -200.256 0.000 0.000
12.00 0.000 -171.648 0.000 0.000
15.00 0.000 -143.040 0.000 0.000
18.00 0.000 -114.432 0.000 0.000
21.00 0.000 -85.824 0.000 0.000
24.00 0.000 -57.216 0.000 0.000
27.00 0.000 -28.608 0.000 0.00030.00 0.000 0.000 0.000 0.000
Support # 4 0.00 0.00
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LRFD Slab Bridge Design, V1.2 Check Page 23 of 34Completed by Kurt Heidenreich, P.E., S.E., KJH Consulting, LLC
******************************************************************************
******** CAST IN PLACE REINFORCED CONCRETE SLAB BRIDGE DESIGN PROGRAM ********
******** Copyright (C) KJH Consulting, LLC, 2008. All Rights Reserved. *******
******** KJH Consulting, LLC ******************************* Page____of____ **
*************************** FATIGUE TRUCK ONLY *******************************
S U M M A R Y T A B L E
Values are 75% of Calculated plus 1.15 Impact Factor______________________________________________________________________________
_______MOMENTS_______ _______SHEAR________ _____REACTIONS_____
LOCATION POSITIVE NEGATIVE POSITIVE NEGATIVE MAXIMUM MINIMUM
(FT) (FT-K/LANE) (FT-K/LANE) (K/LANE) (K/LANE) (K/LANE) (K/LANE)
------------------------------------------------------------------------------
Support # 1 35.59 -3.45
0.00 0.000 0.000 30.697 -2.976
3.00 79.737 -8.928 26.579 -5.433
6.00 135.326 -17.855 22.554 -9.675
9.00 168.041 -26.783 18.671 -13.516
12.00 179.737 -35.711 14.978 -16.967
15.00 172.848 -44.638 11.523 -19.932
18.00 154.207 -53.566 8.567 -23.34421.00 125.599 -62.494 5.981 -26.529
24.00 87.967 -76.147 3.665 -29.299
27.00 44.787 -126.899 1.659 -31.609
30.00 21.625 -184.000 34.093 -33.496
Support # 2 48.78 -3.66
0.00 21.625 -184.000 34.093 -33.496
4.00 41.455 -106.501 30.303 -2.433
8.00 104.821 -56.224 27.706 -4.074
12.00 143.190 -46.493 24.567 -8.623
16.00 165.545 -36.762 20.914 -12.755
20.00 167.946 -27.031 16.876 -16.876
24.00 165.545 -36.762 12.755 -20.914
28.00 143.190 -46.493 8.623 -24.567
32.00 104.821 -56.224 4.074 -27.70636.00 41.455 -106.501 2.433 -30.303
40.00 21.625 -184.000 33.496 -34.093
Support # 3 48.78 -3.66
0.00 21.625 -184.000 33.496 -34.093
3.00 44.787 -126.899 31.609 -1.659
6.00 87.967 -76.147 29.299 -3.665
9.00 125.599 -62.494 26.529 -5.981
12.00 154.207 -53.566 23.344 -8.567
15.00 172.848 -44.638 19.932 -11.523
18.00 179.737 -35.711 16.967 -14.978
21.00 168.041 -26.783 13.516 -18.671
24.00 135.326 -17.855 9.675 -22.554
27.00 79.737 -8.928 5.433 -26.57930.00 0.000 0.000 2.976 -30.697
Support # 4 35.59 -3.45
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LRFD Slab Bridge Design, V1.2 Check Page 24 of 34Completed by Kurt Heidenreich, P.E., S.E., KJH Consulting, LLC
******************************************************************************
******** CAST IN PLACE REINFORCED CONCRETE SLAB BRIDGE DESIGN PROGRAM ********
******** Copyright (C) KJH Consulting, LLC, 2008. All Rights Reserved. *******
******** KJH Consulting, LLC ******************************* Page____of____ **
********************** HL-93 LIVE LOAD ENVELOPE SUMMARY **********************
S U M M A R Y T A B L E
______________________________________________________________________________
_______MOMENTS_______ _______SHEAR________ _____REACTIONS_____
LOCATION POSITIVE NEGATIVE POSITIVE NEGATIVE MAXIMUM MINIMUM
(FT) (FT-K/LANE) (FT-K/LANE) (K/LANE) (K/LANE) (K/LANE) (K/LANE)
------------------------------------------------------------------------------
Support # 1 70.89 -10.60
0.00 0.000 0.000 70.890 -10.596
3.00 182.369 -31.787 59.948 -10.714
6.00 311.257 -63.573 50.428 -17.287
9.00 388.899 -95.360 41.388 -23.795
12.00 418.647 -127.147 32.913 -30.444
15.00 411.951 -158.933 25.088 -38.956
18.00 376.141 -190.720 17.993 -47.26821.00 302.491 -222.507 11.708 -55.271
24.00 197.705 -254.293 6.307 -64.058
27.00 81.645 -294.343 2.933 -73.843
30.00 59.475 -378.961 74.502 -82.880
Support # 2 111.74 -8.65
0.00 59.475 -378.961 88.062 -71.344
4.00 90.095 -209.615 76.472 -6.777
8.00 232.592 -154.998 64.324 -9.202
12.00 355.786 -131.231 52.394 -16.237
16.00 431.404 -122.493 42.606 -24.352
20.00 452.378 -117.552 33.247 -33.247
24.00 431.404 -122.493 24.352 -42.606
28.00 355.786 -131.231 16.237 -52.394
32.00 232.592 -154.998 9.202 -64.32436.00 90.095 -209.615 6.777 -76.472
40.00 59.475 -378.961 71.344 -88.062
Support # 3 111.74 -8.65
0.00 59.475 -378.961 82.880 -74.502
3.00 81.645 -294.343 73.843 -2.933
6.00 197.705 -254.294 64.058 -6.307
9.00 302.491 -222.507 55.271 -11.708
12.00 376.141 -190.720 47.268 -17.993
15.00 411.951 -158.933 38.956 -25.088
18.00 418.647 -127.147 30.444 -32.913
21.00 388.899 -95.360 23.795 -41.388
24.00 311.257 -63.573 17.287 -50.428
27.00 182.369 -31.787 10.714 -59.94830.00 0.000 0.000 10.596 -70.890
Support # 4 70.89 -10.60
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LRFD Slab Bridge Design, V1.2 Check Page 25 of 34Completed by Kurt Heidenreich, P.E., S.E., KJH Consulting, LLC
******************************************************************************
******** CAST IN PLACE REINFORCED CONCRETE SLAB BRIDGE DESIGN PROGRAM ********
******** Copyright (C) KJH Consulting, LLC, 2008. All Rights Reserved. *******
******** KJH Consulting, LLC ******************************* Page____of____ **
*********************** DEAD LOAD & DEFLECTION SUMMARY ***********************
S U M M A R Y T A B L E
MODULUS OF ELASTICITY, E(dead)= 1,200 Ksi, E(live)= 3,640 Ksi______________________________________________________________________________
LOCATION SLAB MOMENT* SLAB DEFLECTION* LIVE LOAD DEFLECTION
(FT) (FT-K/FT) (IN.) (IN.) L over
------------------------------------------------------------------------------
Support # 1, R(Slab)* = 2.70 K/Ft.
0.00 0.000 0.000 0.000 0
3.00 6.965 -0.065 -0.026 13982
6.00 11.681 -0.118 -0.048 7491
9.00 14.146 -0.153 -0.064 5595
12.00 14.361 -0.165 -0.073 4907
15.00 12.326 -0.155 -0.075 4791
18.00 8.042 -0.124 -0.070 5145
21.00 1.507 -0.081 -0.058 620124.00 -7.278 -0.036 -0.040 8949
27.00 -18.313 -0.003 -0.020 18150
30.00 -31.597 0.000 0.000 0
Support # 2, R(Slab)* = 9.80 K/Ft.
0.00 -31.597 0.000 0.000 0
4.00 -13.597 -0.061 -0.036 13212
8.00 0.403 -0.163 -0.075 6382
12.00 10.403 -0.264 -0.108 4429
16.00 16.403 -0.336 -0.130 3703
20.00 18.403 -0.363 -0.136 3518
24.00 16.403 -0.336 -0.130 3703
28.00 10.403 -0.264 -0.108 4429
32.00 0.403 -0.163 -0.075 6382
36.00 -13.597 -0.061 -0.036 1321240.00 -31.597 0.000 0.000 0
Support # 3, R(Slab)* = 9.80 K/Ft.
0.00 -31.597 0.000 0.000 0
3.00 -18.313 -0.003 -0.020 18150
6.00 -7.278 -0.036 -0.040 8949
9.00 1.507 -0.081 -0.058 6201
12.00 8.042 -0.124 -0.070 5145
15.00 12.326 -0.155 -0.075 4791
18.00 14.361 -0.165 -0.073 4907
21.00 14.146 -0.153 -0.064 5595
24.00 11.681 -0.118 -0.048 7491
27.00 6.965 -0.065 -0.026 13982
30.00 0.000 0.000 0.000 0Support # 4, R(Slab)* = 2.70 K/Ft.
* VALUES FOR UNFACTORED SLAB DEAD LOAD @ 250.00 Psf
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LRFD Slab Bridge Design, V1.2 Check Page 26 of 34Completed by Kurt Heidenreich, P.E., S.E., KJH Consulting, LLC
******************************************************************************
******** CAST IN PLACE REINFORCED CONCRETE SLAB BRIDGE DESIGN PROGRAM ********
******** Copyright (C) KJH Consulting, LLC, 2008. All Rights Reserved. *******
******** KJH Consulting, LLC ******************************* Page____of____ **
****************************** SHEAR SUMMARY *********************************
S U M M A R Y T A B L E
All Shear Values are Factored______________________________________________________________________________
SLAB ___INTERIOR STRIP___ __EDGE BEAM STRIP__
LOCATION DEAD MINIMUM MAXIMUM MINIMUM MAXIMUM
(FT) (K/FT) (K/FT) (K/FT) (K/FT) (K/FT)
------------------------------------------------------------------------------
Support # 1
0.00 3.37 2.39 15.23 2.71 16.22
3.00 2.43 1.24 12.38 1.44 13.16
6.00 1.50 -0.92 9.75 -0.89 10.34
9.00 0.56 -3.08 7.20 -3.21 7.60
12.00 -0.38 -5.25 4.73 -5.55 4.96
15.00 -1.32 -7.73 2.37 -8.20 2.42
18.00 -2.25 -10.17 0.12 -10.82 0.0021.00 -3.19 -12.56 -2.00 -13.39 -2.28
24.00 -4.13 -15.07 -3.98 -16.09 -4.42
27.00 -5.07 -17.74 -5.64 -18.95 -6.22
30.00 -6.00 -20.30 4.51 -21.69 4.41
Support # 2
0.00 6.25 -3.71 21.41 -3.56 22.88
4.00 5.00 4.96 18.08 5.50 19.30
8.00 3.75 3.07 14.66 3.44 15.63
12.00 2.50 0.45 11.27 0.62 12.00
16.00 1.25 -2.33 8.22 -2.38 8.72
20.00 0.00 -5.24 5.24 -5.51 5.51
24.00 -1.25 -8.22 2.33 -8.72 2.38
28.00 -2.50 -11.27 -0.45 -12.00 -0.62
32.00 -3.75 -14.66 -3.07 -15.63 -3.4436.00 -5.00 -18.08 -4.96 -19.30 -5.50
40.00 -6.25 -21.41 3.71 -22.88 3.56
Support # 3
0.00 6.00 -4.51 20.30 -4.41 21.69
3.00 5.07 5.64 17.74 6.22 18.95
6.00 4.13 3.98 15.07 4.42 16.09
9.00 3.19 2.00 12.56 2.28 13.39
12.00 2.25 -0.12 10.17 0.00 10.82
15.00 1.32 -2.37 7.73 -2.42 8.20
18.00 0.38 -4.73 5.25 -4.96 5.55
21.00 -0.56 -7.20 3.08 -7.60 3.21
24.00 -1.50 -9.75 0.92 -10.34 0.89
27.00 -2.43 -12.38 -1.24 -13.16 -1.4430.00 -3.37 -15.23 -2.39 -16.22 -2.71
Support # 4
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LRFD Slab Bridge Design, V1.2 Check Page 27 of 34Completed by Kurt Heidenreich, P.E., S.E., KJH Consulting, LLC
******************************************************************************
******** CAST IN PLACE REINFORCED CONCRETE SLAB BRIDGE DESIGN PROGRAM ********
******** Copyright (C) KJH Consulting, LLC, 2008. All Rights Reserved. *******
******** KJH Consulting, LLC ******************************* Page____of____ **
*********** INTERIOR STRIP DESIGN MOMENTS AND REQ'D STEEL SUMMARY ************
S U M M A R Y T A B L E
______________________________________________________________________________
___FACTORED MOMENTS___ __STEEL REQ'D__ ___FATIGUE MOMENTS___
LOCATION POSITIVE NEGATIVE POS. NEG. MAXIMUM MINIMUM
(FT) (#-IN/FT) (#-IN/FT) (SQ. IN. /FT) (#-IN/FT) (#-IN/FT)
------------------------------------------------------------------------------
Support # 1
0.00 0.0 0.0 0.00+ 0.00+ 0.0 0.0
3.00 470767.0 65777.5 0.68+ 0.00 158174.0 91675.4
6.00 799730.9 90888.8 0.88< 0.00 266459.5 151573.8
9.00 991117.2 75334.0 1.10< 0.00 325813.1 179695.4
12.00 1051264.0 19113.1 1.17< 0.00 337625.7 176040.1
15.00 1001827.0 -77774.2 1.12< 0.11+ 303722.8 140607.7
18.00 856665.3 -215327.4 0.95< 0.32+ 229228.1 73398.521.00 599278.5 -393546.8 0.78= 0.58+ 115482.2 -25587.6
24.00 242343.4 -612432.4 0.35+ 0.80= -36809.6 -159894.5
27.00 -176578.8 -887609.6 0.00 1.01< -225039.0 -353803.3
30.00 -458610.0 -1287737.0 0.00 1.50< -430031.6 -584250.0
Support # 2
0.00 -458610.0 -1287737.0 0.00 1.50< -430031.6 -584250.0
4.00 -75375.8 -642157.6 0.00 0.80= -160943.5 -271910.4
8.00 447135.6 -285836.4 0.65+ 0.42+ 84304.3 -36479.5
12.00 860846.6 -60153.5 0.95< 0.09+ 254311.9 112049.6
16.00 1112291.0 64814.9 1.25< 0.00 355816.3 204086.3
20.00 1188102.0 110306.9 1.34< 0.00 385863.3 239630.7
24.00 1112291.0 64815.0 1.25< 0.00 355816.3 204086.4
28.00 860846.6 -60153.5 0.95< 0.09+ 254311.9 112049.6
32.00 447135.6 -285836.4 0.65+ 0.42+ 84304.3 -36479.536.00 -75375.8 -642157.6 0.00 0.80= -160943.6 -271910.4
40.00 -458610.0 -1287737.0 0.00 1.50< -430031.6 -584250.0
Support # 3
0.00 -458610.0 -1287737.0 0.00 1.50< -430031.6 -584250.0
3.00 -176578.8 -887609.5 0.00 1.01< -225039.0 -353803.3
6.00 242343.4 -612432.4 0.35+ 0.80= -36809.6 -159894.5
9.00 599278.5 -393546.8 0.78= 0.58+ 115482.2 -25587.6
12.00 856665.3 -215327.5 0.95< 0.32+ 229228.1 73398.5
15.00 1001827.0 -77774.2 1.12< 0.11+ 303722.9 140607.8
18.00 1051264.0 19113.0 1.17< 0.00 337625.6 176040.0
21.00 991117.3 75334.0 1.10< 0.00 325813.1 179695.4
24.00 799730.9 90888.8 0.88< 0.00 266459.6 151573.9
27.00 470767.0 65777.5 0.68+ 0.00 158174.0 91675.430.00 0.0 0.0 0.00+ 0.00 0.0 0.0
Support # 4
< ULTIMATE STRENGTH MOMENT CONTROLS AREA OF STEEL
= AREA OF STEEL IS EQUAL TO 1.2 X CRACKING MOMENT STRENGTH
+ AREA OF STEEL IS 1/3 MORE THAN REQUIRED BUT LESS THAN 1.2 MCR
> FATIGUE STRESS RANGE UNDER SERVICE MOMENTS CONTROLS AREA OF STEEL
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LRFD Slab Bridge Design, V1.2 Check Page 28 of 34Completed by Kurt Heidenreich, P.E., S.E., KJH Consulting, LLC
******************************************************************************
******** CAST IN PLACE REINFORCED CONCRETE SLAB BRIDGE DESIGN PROGRAM ********
******** Copyright (C) KJH Consulting, LLC, 2008. All Rights Reserved. *******
******** KJH Consulting, LLC ******************************* Page____of____ **
*********************** INTERIOR STRIP BOTTOM STEEL **************************
-----------------ALL DISTANCES MEASURED FROM LEFT END OF SPAN-----------------
80% OF Mcr = 307200 IN-#/Ft
REINFORCING IS SPACED AT 6.00 IN.
BAR 1 IS CONTINUOUS. DEVELOP INTO SUPPORTS
----------------------------------- SPAN #1 -----------------------------------
BOTTOM TRANSVERSE DISTRIBUTION AREA OF STEEL = 0.21 Sq. In./Ft.
BAR 1 IS A # 7, AND BAR 2 IS A # 7
MAX. As(Req'd) IS 1.17 Sq In /Ft AND As(Prov.) IS 1.20 Sq In /Ft
MAXIMUM Ms = 655225 IN-#/Ft, SMAX =11.02 IN.
REQUIRED BAR EXTENSION = 18.00 IN.
BAR 2 BEGINS AT 1.14 FT. AND ENDS AT 23.74 FT.
BEGINNING CUT Ms = 112650 IN-#/Ft < 80% Mcr
ENDING CUT Ms = 131807 IN-#/Ft < 80% Mcr
----------------------------------- SPAN #2 -----------------------------------
BOTTOM TRANSVERSE DISTRIBUTION AREA OF STEEL = 0.21 Sq. In./Ft.
BAR 1 IS A # 8, AND BAR 2 IS A # 7
MAX. As(Req'd) IS 1.34 Sq In /Ft AND As(Prov.) IS 1.39 Sq In /Ft
MAXIMUM Ms = 748757 IN-#/Ft, SMAX =11.00 IN.
REQUIRED BAR EXTENSION = 24.00 IN.
BAR 2 BEGINS AT 7.88 FT. AND ENDS AT 32.12 FT.
BEGINNING CUT Ms = 246880 IN-#/Ft < 80% Mcr
ENDING CUT Ms = 246880 IN-#/Ft < 80% Mcr
----------------------------------- SPAN #3 -----------------------------------
BOTTOM TRANSVERSE DISTRIBUTION AREA OF STEEL = 0.21 Sq. In./Ft.BAR 1 IS A # 7, AND BAR 2 IS A # 7
MAX. As(Req'd) IS 1.17 Sq In /Ft AND As(Prov.) IS 1.20 Sq In /Ft
MAXIMUM Ms = 655225 IN-#/Ft, SMAX =11.02 IN.
REQUIRED BAR EXTENSION = 18.00 IN.
BAR 2 BEGINS AT 6.26 FT. AND ENDS AT 28.86 FT.
BEGINNING CUT Ms = 131807 IN-#/Ft < 80% Mcr
ENDING CUT Ms = 112650 IN-#/Ft < 80% Mcr
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LRFD Slab Bridge Design, V1.2 Check Page 29 of 34Completed by Kurt Heidenreich, P.E., S.E., KJH Consulting, LLC
******************************************************************************
******** CAST IN PLACE REINFORCED CONCRETE SLAB BRIDGE DESIGN PROGRAM ********
******** Copyright (C) KJH Consulting, LLC, 2008. All Rights Reserved. *******
******** KJH Consulting, LLC ******************************* Page____of____ **
************************* INTERIOR STRIP TOP STEEL ***************************
TOP TRANSVERSE TEMPERATURE & SHRINKAGE AREA OF STEEL = 0.11 Sq. In./Ft.
LAP # 4 BAR LONGITUDINAL T&S STEEL WITH BAR 1, As = 0.20 Sq. In./Ft.
-----------------ALL DISTANCES MEASURED FROM LEFT END OF SPAN-----------------
80% OF Mcr = 307200 IN-#/Ft
REINFORCING IS SPACED AT 6.00 IN.
--------------------------------- SUPPORT #2 ----------------------------------
BAR 1 IS A # 9, AND BAR 2 IS A # 7
MAX. As(Req'd) IS 1.50 Sq In /Ft AND As(Prov.) IS 1.60 Sq In /Ft
MAXIMUM Ms = 855766 IN-#/Ft, SMAX = 6.01 IN.
SPAN #1 REQUIRED EXTENSION FOR BAR 1 = 22.50 IN., BAR 2 18.00 IN.
SPAN #2 REQUIRED EXTENSION FOR BAR 1 = 30.00 IN., BAR 2 24.00 IN.
BAR 1 BEGINS AT 10.13 FT. SPAN #1 AND ENDS AT 18.50 FT. SPAN #2
BAR 2 BEGINS AT 23.60 FT. SPAN #1 AND ENDS AT 4.97 FT. SPAN #2
BEGINNING CUT Ms = 356365 IN-#/Ft, SMAX =12.09 IN.
ENDING CUT Ms = 356133 IN-#/Ft, SMAX =12.10 IN.
--------------------------------- SUPPORT #3 ----------------------------------
BAR 1 IS A # 9, AND BAR 2 IS A # 7
MAX. As(Req'd) IS 1.50 Sq In /Ft AND As(Prov.) IS 1.60 Sq In /Ft
MAXIMUM Ms = 855766 IN-#/Ft, SMAX = 6.01 IN.
SPAN #2 REQUIRED EXTENSION FOR BAR 1 = 30.00 IN., BAR 2 24.00 IN.
SPAN #3 REQUIRED EXTENSION FOR BAR 1 = 22.50 IN., BAR 2 18.00 IN.
BAR 1 BEGINS AT 21.50 FT. SPAN #2 AND ENDS AT 19.88 FT. SPAN #3
BAR 2 BEGINS AT 35.03 FT. SPAN #2 AND ENDS AT 6.40 FT. SPAN #3BEGINNING CUT Ms = 356133 IN-#/Ft, SMAX =12.10 IN.
ENDING CUT Ms = 356365 IN-#/Ft, SMAX =12.09 IN.
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LRFD Slab Bridge Design, V1.2 Check Page 30 of 34Completed by Kurt Heidenreich, P.E., S.E., KJH Consulting, LLC
******************************************************************************
******** CAST IN PLACE REINFORCED CONCRETE SLAB BRIDGE DESIGN PROGRAM ********
******** Copyright (C) KJH Consulting, LLC, 2008. All Rights Reserved. *******
******** KJH Consulting, LLC ******************************* Page____of____ **
************** EDGE BEAM DESIGN MOMENTS AND REQ'D STEEL SUMMARY **************
S U M M A R Y T A B L E
______________________________________________________________________________
___FACTORED MOMENTS___ __STEEL REQ'D__ ___FATIGUE MOMENTS___
LOCATION POSITIVE NEGATIVE POS. NEG. MAXIMUM MINIMUM
(FT) (#-IN/FT) (#-IN/FT) (SQ. IN. /FT) (#-IN/FT) (#-IN/FT)
------------------------------------------------------------------------------
Support # 1
0.00 0.0 0.0 0.00+ 0.00+ 0.0 0.0
3.00 489797.0 77838.0 0.71+ 0.00 168787.9 102289.3
6.00 831286.1 110992.7 0.92< 0.00 284258.8 169373.1
9.00 1028914.0 99464.2 1.15< 0.00 347369.0 201251.3
12.00 1089350.0 43252.5 1.22< 0.00 359509.6 197924.1
15.00 1035384.0 -57642.7 1.15< 0.08+ 322506.3 159391.1
18.00 881599.3 -203221.0 0.98< 0.30+ 241482.3 85652.721.00 610633.1 -393482.7 0.78= 0.58+ 117778.5 -23291.3
24.00 235825.5 -628427.6 0.34+ 0.80= -47899.7 -170984.7
27.00 -207321.6 -920474.3 0.00 1.05< -252944.2 -381708.6
30.00 -513812.7 -1337582.0 0.00 1.57< -478180.5 -632399.0
Support # 2
0.00 -513812.7 -1337582.0 0.00 1.57< -478180.5 -632399.0
4.00 -95887.3 -665073.3 0.00 0.80= -181663.5 -292630.3
8.00 458040.0 -288124.4 0.66+ 0.43+ 84918.1 -35865.7
12.00 889973.1 -42879.4 0.99< 0.06+ 270164.0 127901.7
16.00 1152132.0 120940.9 1.29< 0.00 380811.4 229081.4
20.00 1231096.0 205324.3 1.39< 0.00 413906.1 267673.5
24.00 1152133.0 120941.0 1.29< 0.00 380811.5 229081.5
28.00 889973.1 -42879.4 0.99< 0.06+ 270164.0 127901.7
32.00 458040.0 -288124.4 0.66+ 0.43+ 84918.1 -35865.836.00 -95887.3 -665073.4 0.00 0.80= -181663.5 -292630.3
40.00 -513812.7 -1337582.0 0.00 1.57< -478180.5 -632399.0
Support # 3
0.00 -513812.7 -1337582.0 0.00 1.57< -478180.5 -632399.0
3.00 -207321.5 -920474.3 0.00 1.05< -252944.2 -381708.5
6.00 235825.4 -628427.6 0.34+ 0.80= -47899.7 -170984.7
9.00 610633.1 -393482.7 0.78= 0.58+ 117778.5 -23291.3
12.00 881599.3 -203221.1 0.98< 0.30+ 241482.3 85652.7
15.00 1035384.0 -57642.7 1.15< 0.08+ 322506.3 159391.1
18.00 1089350.0 43252.4 1.22< 0.00 359509.6 197924.0
21.00 1028914.0 99464.2 1.15< 0.00 347369.0 201251.3
24.00 831286.1 110992.8 0.92< 0.00 284258.8 169373.1
27.00 489797.1 77838.0 0.71+ 0.00 168787.9 102289.330.00 0.0 0.0 0.00+ 0.00 0.0 0.0
Support # 4
< ULTIMATE STRENGTH MOMENT CONTROLS AREA OF STEEL
= AREA OF STEEL IS EQUAL TO 1.2 X CRACKING MOMENT STRENGTH
+ AREA OF STEEL IS 1/3 MORE THAN REQUIRED BUT LESS THAN 1.2 MCR
> FATIGUE STRESS RANGE UNDER SERVICE MOMENTS CONTROLS AREA OF STEEL
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LRFD Slab Bridge Design, V1.2 Check Page 31 of 34Completed by Kurt Heidenreich, P.E., S.E., KJH Consulting, LLC
******************************************************************************
******** CAST IN PLACE REINFORCED CONCRETE SLAB BRIDGE DESIGN PROGRAM ********
******** Copyright (C) KJH Consulting, LLC, 2008. All Rights Reserved. *******
******** KJH Consulting, LLC ******************************* Page____of____ **
************************* EDGE BEAM BOTTOM STEEL *****************************
-----------------ALL DISTANCES MEASURED FROM LEFT END OF SPAN-----------------
80% OF Mcr = 307200 IN-#/Ft
REINFORCING IS SPACED AT 5.90 IN.
BAR 1 IS CONTINUOUS. DEVELOP INTO SUPPORTS
----------------------------------- SPAN #1 -----------------------------------
BAR 1 IS A # 7, AND BAR 2 IS A # 7
MAX. As(Req'd) IS 1.22 Sq In /Ft AND As(Prov.) IS 1.22 Sq In /Ft
MAXIMUM Ms = 684221 IN-#/Ft, SMAX =10.64 IN.
REQUIRED BAR EXTENSION = 18.00 IN.
BAR 2 BEGINS AT 1.08 FT. AND ENDS AT 23.64 FT.
BEGINNING CUT Ms = 111731 IN-#/Ft < 80% Mcr
ENDING CUT Ms = 133756 IN-#/Ft < 80% Mcr
----------------------------------- SPAN #2 -----------------------------------
BAR 1 IS A # 8, AND BAR 2 IS A # 7
MAX. As(Req'd) IS 1.39 Sq In /Ft AND As(Prov.) IS 1.41 Sq In /Ft
MAXIMUM Ms = 782593 IN-#/Ft, SMAX =10.61 IN.
REQUIRED BAR EXTENSION = 24.00 IN.
BAR 2 BEGINS AT 7.75 FT. AND ENDS AT 32.25 FT.
BEGINNING CUT Ms = 239804 IN-#/Ft < 80% Mcr
ENDING CUT Ms = 239804 IN-#/Ft < 80% Mcr
----------------------------------- SPAN #3 -----------------------------------
BAR 1 IS A # 7, AND BAR 2 IS A # 7
MAX. As(Req'd) IS 1.22 Sq In /Ft AND As(Prov.) IS 1.22 Sq In /Ft
MAXIMUM Ms = 684221 IN-#/Ft, SMAX =10.64 IN.REQUIRED BAR EXTENSION = 18.00 IN.
BAR 2 BEGINS AT 6.36 FT. AND ENDS AT 28.92 FT.
BEGINNING CUT Ms = 133756 IN-#/Ft < 80% Mcr
ENDING CUT Ms = 111731 IN-#/Ft < 80% Mcr
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LRFD Slab Bridge Design, V1.2 Check Page 32 of 34Completed by Kurt Heidenreich, P.E., S.E., KJH Consulting, LLC
******************************************************************************
******** CAST IN PLACE REINFORCED CONCRETE SLAB BRIDGE DESIGN PROGRAM ********
******** Copyright (C) KJH Consulting, LLC, 2008. All Rights Reserved. *******
******** KJH Consulting, LLC ******************************* Page____of____ **
*************************** EDGE BEAM TOP STEEL ******************************
LAP # 4 BAR LONGITUDINAL T&S STEEL WITH BAR 1, As = 0.21 Sq. In./Ft.
-----------------ALL DISTANCES MEASURED FROM LEFT END OF SPAN-----------------80% OF Mcr = 307200 IN-#/Ft
REINFORCING IS SPACED AT 5.70 IN.
--------------------------------- SUPPORT #2 ----------------------------------
BAR 1 IS A # 9, AND BAR 2 IS A # 7
MAX. As(Req'd) IS 1.57 Sq In /Ft AND As(Prov.) IS 1.68 Sq In /Ft
MAXIMUM Ms = 900162 IN-#/Ft, SMAX = 5.99 IN.
SPAN #1 REQUIRED EXTENSION FOR BAR 1 = 22.50 IN., BAR 2 18.00 IN.
SPAN #2 REQUIRED EXTENSION FOR BAR 1 = 30.00 IN., BAR 2 24.00 IN.
BAR 1 BEGINS AT 10.13 FT. SPAN #1 AND ENDS AT 18.50 FT. SPAN #2
BAR 2 BEGINS AT 23.59 FT. SPAN #1 AND ENDS AT 4.99 FT. SPAN #2
BEGINNING CUT Ms = 366702 IN-#/Ft, SMAX =11.58 IN.
ENDING CUT Ms = 370283 IN-#/Ft, SMAX =11.40 IN.
--------------------------------- SUPPORT #3 ----------------------------------
BAR 1 IS A # 9, AND BAR 2 IS A # 7
MAX. As(Req'd) IS 1.57 Sq In /Ft AND As(Prov.) IS 1.68 Sq In /Ft
MAXIMUM Ms = 900162 IN-#/Ft, SMAX = 5.99 IN.
SPAN #2 REQUIRED EXTENSION FOR BAR 1 = 30.00 IN., BAR 2 24.00 IN.
SPAN #3 REQUIRED EXTENSION FOR BAR 1 = 22.50 IN., BAR 2 18.00 IN.
BAR 1 BEGINS AT 21.50 FT. SPAN #2 AND ENDS AT 19.88 FT. SPAN #3
BAR 2 BEGINS AT 35.01 FT. SPAN #2 AND ENDS AT 6.41 FT. SPAN #3BEGINNING CUT Ms = 370284 IN-#/Ft, SMAX =11.40 IN.
ENDING CUT Ms = 366702 IN-#/Ft, SMAX =11.58 IN.
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LRFD Slab Bridge Design, V1.2 Check Page 33 of 34Completed by Kurt Heidenreich, P.E., S.E., KJH Consulting, LLC
******************************************************************************
******** CAST IN PLACE REINFORCED CONCRETE SLAB BRIDGE DESIGN PROGRAM ********
******** Copyright (C) KJH Consulting, LLC, 2008. All Rights Reserved. *******
******** KJH Consulting, LLC ******************************* Page____of____ **
*************************** SUPPORT # 1 DESIGN *******************************
-------------------------------{ DIMENSIONS }--------------------------------
[ CAP SUPPORT TYPE ]TOP WIDTH, b(+) = 24.00 In.
DISTANCE TO BOTTOM STEEL CENTROID = 4.00 In.
POSITIVE MOMENT EFFECTIVE DEPTH, d[+] = 33.00 In.
BOTTOM WIDTH, b(-) = 30.00 In.
DISTANCE TO TOP STEEL CENTROID = 6.00 In.
NEGATIVE MOMENT EFFECTIVE DEPTH, d[-] = 32.00 In.
CAP DROP = 18.00 In.
PAVEMENT DEAD LOAD = 1.00 Klf
---------------------------{ REINFORCING SUMMARY }----------------------------
NOTE: Top and Bottom Cracking Moment Based on Slab Depth + Cap Drop
(Top Steel)MAXIMUM FACTORED NEGATIVE MOMENT = 1006531.0 In-#
MAX. FACTORED NEGATIVE OVERHANG MOMENT = 935105.7 In-#
REQ'D AREA OF STEEL(-), TOP = 0.59 In. Sq.
REQ'D OVERHANG AREA OF STEEL(-), TOP = 0.55 In. Sq.
MIN. AREA OF STEEL, TOP (1.2Mcr) = 3.85 In. Sq.
(Bottom Steel)
MAXIMUM FACTORED POSITIVE MOMENT = 1050986.0 In-#
REQ'D AREA OF STEEL(+), BOTTOM = 0.60 In. Sq.
MIN. AREA OF STEEL, BOTTOM (1.2Mcr) = 2.98 In. Sq.
(Shear Steel)
EFFECTIVE SHEAR DEPTH, dv = 20.00 In. AND WIDTH, bv = 24.00 In.
MAXIMUM FACTORED OVERHANG SHEAR = 68.01 KipsMAXIMUM FACTORED INTERIOR SHEAR = 91.50 Kips
CONCRETE SHEAR STRENGTH(PHI Vc) = 54.60 Kips
REQUIRED OVERHANG SHEAR STIRRUP AREA = 0.15 In. Sq. / Ft. (BOTH LEGS)
REQUIRED INTERIOR SHEAR STIRRUP AREA = 0.41 In. Sq. / Ft. (BOTH LEGS)
MINIMUM REQUIRED SHEAR STIRRUP AREA = 0.30 In. Sq. / Ft. (BOTH LEGS)
----------------------------{ PILE LOAD SUMMARY }-----------------------------
CAP TYPE SUPPORT IS ASSUMED TO BE FLEXIBLE FOR PILE LOAD CALCULATIONS
6 - PILES @ 6 Ft.- 6 In. SPACING WITH 3.25 Ft. OVERHANGS / SIDE
MAXIMUM UNFACTORED WHEEL LOAD = 16.00 Kips
DYNAMIC LOAD ALLOWANCE IS NOT INCLUDED IN PILE LOADS
MAXIMUM FACTORED LIVE LOAD REACTION = 97.10 Kips/Lane
MINIMUM FACTORED LIVE LOAD REACTION = -14.76 Kips/Lane
MAXIMUM FACTORED EXTERIOR PILE LOAD = 101.79 Kips
MINIMUM FACTORED EXTERIOR PILE LOAD = 103.91 Kips
REACTION WITH MINIMUM LIVE LOAD IS 138.71 Kips or 23.12 Kips/Pile
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******************************************************************************
******** CAST IN PLACE REINFORCED CONCRETE SLAB BRIDGE DESIGN PROGRAM ********
******** Copyright (C) KJH Consulting, LLC, 2008. All Rights Reserved. *******
******** KJH Consulting, LLC ******************************* Page____of____ **
*************************** SUPPORT # 2 DESIGN *******************************
-------------------------------{ DIMENSIONS }--------------------------------
[ WALL SUPPORT TYPE ]
WALL WIDTH = 24.00 In.
CAP DROP =144.00 In.
---------------------------{ REINFORCING SUMMARY }----------------------------
THE MINIMUM AREA OF STEEL FOR TEMPERATURE AND SHRINKAGE IS
b = 24.00 Inches, h = 39.00 Feet
As (T&S) = 1.3bh/2(b+h)Fy = 0.25 In. Sq. / Ft. / Face
b = 24.00 Inches, h = 144.00 Inches
As (T&S) = 1.3bh/2(b+h)Fy = 0.22 In. Sq. / Ft. / Face
REINFORCING MUST BE PROVIDED ON EACH FACE BOTH HORIZONTALLY AND VERTICALLY
----------------------------{ PILE LOAD SUMMARY }-----------------------------
WALL TYPE SUPPORT IS ASSUMED TO BE RIGID FOR PILE LOAD CALCULATIONS
7 - PILES @ 6 Ft.- 0 In. SPACING WITH 1.50 Ft. OVERHANGS / SIDE
MAXIMUM UNFACTORED WHEEL LOAD = 16.00 Kips
DYNAMIC LOAD ALLOWANCE IS NOT INCLUDED IN PILE LOADS
MAXIMUM FACTORED LIVE LOAD REACTION = 158.53 Kips/Lane
MINIMUM FACTORED LIVE LOAD REACTION = -12.02 Kips/Lane
MAXIMUM FACTORED EXTERIOR PILE LOAD = 200.12 Kips
MINIMUM FACTORED EXTERIOR PILE LOAD = 95.38 Kips
REACTION WITH MINIMUM LIVE LOAD IS 474.65 Kips or 67.81 Kips/Pile