lrfd slab bridge design check

7/29/2019 LRFD Slab Bridge Design Check

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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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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


3/34


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


4/34


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.)


5/34


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


6/34


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)


7/34


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


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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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


9/34


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


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.


10/34


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)


11/34


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


12/34


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)


13/34


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


14/34


= 0.85 x (1 - ( 1 2.36 x Ku ) ) = 0.06029 = x fc / fy = 0.00402


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


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


15/34


= 0.85 x (1 - ( 1 2.36 x Ku ) ) = 0.0566 = x fc / fy = 0.00377


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


16/34


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


17/34


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)


18/34


OUPUT FILE

REPORT


19/34


******************************************************************************

******** 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.



-------------------------------{ 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


20/34


******************************************************************************




********************* 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


21/34


******************************************************************************




************************ TANDEM WITH LANE LOADING ****************************


Includes 1.33 Impact Factor on Tandem Load______________________________________________________________________________




------------------------------------------------------------------------------

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


22/34


******************************************************************************




********************** TWIN TRUCKS WITH LANE LOADING *************************


90% of Twin Trucks (with 1.33 Impact Factor) + 90% of Lane Load______________________________________________________________________________




------------------------------------------------------------------------------

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


23/34


******************************************************************************




*************************** FATIGUE TRUCK ONLY *******************************


Values are 75% of Calculated plus 1.15 Impact Factor______________________________________________________________________________




------------------------------------------------------------------------------

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


24/34


******************************************************************************




********************** HL-93 LIVE LOAD ENVELOPE SUMMARY **********************


______________________________________________________________________________




------------------------------------------------------------------------------

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


25/34


******************************************************************************




*********************** DEAD LOAD & DEFLECTION SUMMARY ***********************


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


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


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


26/34


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****************************** SHEAR SUMMARY *********************************


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


27/34


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*********** INTERIOR STRIP DESIGN MOMENTS AND REQ'D STEEL SUMMARY ************


______________________________________________________________________________

___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


28/34


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*********************** 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.








----------------------------------- SPAN #3 -----------------------------------

BOTTOM TRANSVERSE DISTRIBUTION AREA OF STEEL = 0.21 Sq. In./Ft.BAR 1 IS A # 7, AND BAR 2 IS A # 7








29/34


******************************************************************************




************************* 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.


80% OF Mcr = 307200 IN-#/Ft


--------------------------------- SUPPORT #2 ----------------------------------



MAXIMUM Ms = 855766 IN-#/Ft, SMAX = 6.01 IN.

SPAN #1 REQUIRED EXTENSION FOR BAR 1 = 22.50 IN., BAR 2 18.00 IN.


BAR 1 BEGINS AT 10.13 FT. SPAN #1 AND ENDS AT 18.50 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 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.



30/34


******************************************************************************




************** EDGE BEAM DESIGN MOMENTS AND REQ'D STEEL SUMMARY **************


______________________________________________________________________________

___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


31/34


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************************* EDGE BEAM BOTTOM STEEL *****************************


80% OF Mcr = 307200 IN-#/Ft


BAR 1 IS CONTINUOUS. DEVELOP INTO SUPPORTS

----------------------------------- SPAN #1 -----------------------------------








----------------------------------- SPAN #2 -----------------------------------








----------------------------------- SPAN #3 -----------------------------------



MAXIMUM Ms = 684221 IN-#/Ft, SMAX =10.64 IN.REQUIRED BAR EXTENSION = 18.00 IN.





32/34


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*************************** 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


--------------------------------- SUPPORT #2 ----------------------------------








BEGINNING CUT Ms = 366702 IN-#/Ft, SMAX =11.58 IN.


--------------------------------- SUPPORT #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.



33/34


******************************************************************************




*************************** 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


34/34

******************************************************************************




*************************** 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

lrfd slab bridge design check

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