U.S. Department of Transportation
1200 New Jersey Avenue, SE
Washington, DC 20590
202-366-4000

# Bridges & Structures

## Section A5 - Comparison Between the Hand Calculations and the Two Computer Programs

### Moment Comparison

Method Location Girder Slab, Haunch and Ext. Diaphragm Parapets FWS Positive
LL(3)
Negative
LL(4)
(ft.) (k-ft) (k-ft) (k-ft) (k-ft) (k-ft) (k-ft)
Opis 11 615.5 (1) 649.8 (1) 84.9 102.2 878.4 -
Qcon - (5) - (5) - 114.0 909.3 -
Table 5.3 656.0 (2) 643.0 (2) 85.0 114.0 886.0 -

Opis 55 1,709.5 (1) 1,864.8 (1) 163.4 196.6 2004.3 -
QCon - - - 219.3 2,063.0 -
Table 5.3 1,725.0 (2) 1,832.0 (2) 164.0 220.0 2,010.0 -

Opis ≈ 110 0 0 -326.7 -393.3 - -2,098.8
QCon - - - -438.6 - -2,096.9
Table 5.3 0 0 -326.0 -438.0 - -2,095.0

### Shear Comparison

Method Location Girder Slab, Haunch and Ext. Diaphragm Parapets FWS Positive
LL(3)
Negative
LL(4)
(ft.) (k) (k) (k) (k) (k) (k)
Opis 11 49.7 (1) 52.8 (1) 6.5 7.9 95.9 -14.9
QCon - (5) - (5) - (5) 8.8 99.4 -13.0
Table 5.3 49.2 (2) 52.2 (2) 6.5 8.8 95.5 -13.4

Opis 55 0 (1) -2.5 (1) -3.0 -3.6 36.2 -60.5
QCon - - - -4.0 36.7 -61.7
Table 5.3 -0.6 (2) -3.1 (2) -3.0 -4.0 36.2 -61.2

Opis ≈ 110 0 0 -14.9 -17.9 0 -130.9
QCon - - - -19.9 0 -132.1
Table 5.3 0 0 -14.8 -19.9 0 -131.1

#### Notes:

1. Calculated based on a 110 ft simple span length and the force effects are calculated at the distance shown in the table measured from the centerline of the abutment neoprene pads.
2. Calculated based on a 109 ft simple span length (distance between the centerline of the neoprene pads) and the force effects are calculated at the distance shown in the table measured from the centerline of the abutment neoprene pads.
3. Truck + Lane including impact
4. 0.90(Truck Pair + Lane including impact) as specified in S3.6.1.3.1
5. QConBridge does not apply the noncomposite loads to the simple span girder, the program applies the girder, slab, haunch and diaphragm loads to the continuous girder, therefore, these results are not comparable.

## Section A6 - Flexural Resistance Sample Calculation from Opis to Compare with Hand Calculations

The following is sample Opis output for flexure at 55 ft. and 110 ft. from the end bearing. These results may be compared to the hand calculations in Design Step 5.6 for the positive and negative regions.

### Positive Bending Region

```PERFORMING AASHTO LRFD SPECIFICATION CHECKS - 5.7.3.2 Flexural Resistance
Point of Interest : 105.00 (55.0 ft.)
Construction Stage: 2
Prestress Summary:
dp = 74.502 in (from top)
Aps = 6.732 in^2
fps = 264.532 ksi (avg. for all rows)
POSITIVE Flexural Resistance:
** Analyzed as a RECTANGULAR Section **
Layer Area, in^2 Stress, ksi Force, kips Lever-Arm, in Moment i, in-k
-----------------------------------------------------------------------------------
CS 507.832 -0.85*f'c -1726.627 3.095 5343.728
RT 2.000 -32.515 -65.029 2.132 138.670
RB 3.720 2.911 10.828 -0.180 1.950
PS11 0.612 264.145 161.657 -64.118 10365.045
PS10 0.918 264.309 242.636 -66.118 16042.478
PS 9 0.306 264.464 80.926 -68.118 5512.478
PS 8 0.306 264.464 80.926 -68.118 5512.478
PS 7 0.918 264.464 242.778 -68.118 16537.434
PS 6 0.306 264.610 80.971 -70.118 5677.476
PS 5 0.306 264.610 80.971 -70.118 5677.476
PS 4 1.224 264.610 323.883 -70.118 22709.904
PS 3 0.306 264.750 81.013 -72.118 5842.487
PS 2 0.306 264.750 81.013 -72.118 5842.487
PS 1 1.224 264.750 324.053 -72.118 23369.949
-----------------------------------------------------------------------------------
Sum -0.002 128574.031
Flexural Resistance Summary:
beta 1 = 0.850 phi f = 1.000
c = 5.382 in Mn = 128574.031 in-k
a = 4.575 in (from top) = 10714.503 ft-k
f'c = 4.000 ksi (slab) phi*Mn = 128574.031 in-k
[AASHTO LRFD (5.7.3.2.1-1)]
= 10714.503 ft-k
(COMPARED TO 10,697 ft-k from hand calculations)
Effective Shear Depth: [AASHTO LRFD 5.8.2.7]
Tensile Force = 1791.655 kips
dv = Mn / Tensile Force = 71.763 in
Tensile Capacity of Reinforcement on Flexural Tension Side: [AASHTO 5.8.3.5]
Rebar = 0.000 kips
P/S = 1780.827 kips
T(Cap) = 1780.827 kips
Layer Codes:
=> C_ : C = Concrete, where _ may be:
S = Slab, TF = Top Flange, W = Web, BF = Bottom Flange,
^T = Top fillets and tapers, ^B = Bottom fillets and tapers
=> R_ : R = Reinforcement, where _ is the row number (1-5, B (bottom), T (top))
=> PS_ : PS = Prestress, where _ is the row number
Notes:
=> The flexural resistance is determined based on:
* Equilibrium
* Strain compatibility
* Strain in extreme compressive concrete fiber is 0.003
=> The stress in the mild compression steel includes an adjustment for
the displaced concrete. fs = (es * Es) + (0.85 f'c ABS(es / ey))```

### Negative Bending Region

```PERFORMING AASHTO LRFD SPECIFICATION CHECKS - 5.7.3.2 Flexural Resistance
Point of Interest : 110.00 (110.0 ft.)
Construction Stage: 2
NEGATIVE Flexural Resistance:
** Analyzed as a RECTANGULAR Section **
Layer Area, in^2 Stress, ksi Force, kips Lever-Arm, in Moment i, in-k
-----------------------------------------------------------------------------------
RB 14.520 60.000 871.200 -67.445 58757.660
R1 1.550 -37.650 -58.358 3.590 209.478
CBF 159.381 -0.85*f'c -812.843 4.743 3855.703
-----------------------------------------------------------------------------------
Sum 0.000 62822.840
Flexural Resistance Summary:
beta 1 = 0.750 phi f = 0.900
c = 7.590 in Mn = 62822.840 in-k
a = 5.692 in (from bottom) = 5235.237 ft-k
phi*Mn = 56540.555 in-k
[AASHTO LRFD (5.7.3.2.1-1)]
= 4711.713 ft-k
(COMPARED TO 4,775 ft-k from hand calculations)
f'c = 6.000 ksi (flange)
f'c = 6.000 ksi (stem)
Effective Shear Depth: [AASHTO LRFD 5.8.2.7]
Tensile Force = 871.200 kips
dv = Mn / Tensile Force = 72.111 in
Tensile Capacity of Reinforcement on Flexural Tension Side: [AASHTO 5.8.3.5]
Rebar = 871.200 kips
T(Cap) = 871.200 kips
Layer Codes:
=> C_ : C = Concrete, where _ may be:
S = Slab, TF = Top Flange, W = Web, BF = Bottom Flange,
^T = Top fillets and tapers, ^B = Bottom fillets and tapers
=> R_ : R = Reinforcement, where _ is the row number (1-5, B (bottom), T (top))
=> PS_ : PS = Prestress, where _ is the row number
Notes:
=> The flexural resistance is determined based on:
* Equilibrium
* Strain compatibility
* Strain in extreme compressive concrete fiber is 0.003
=> The stress in the mild compression steel includes an adjustment for
the displaced concrete. fs = (es * Es) + (0.85 f'c ABS(es / ey))```
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Updated: 06/23/2015
Federal Highway Administration | 1200 New Jersey Avenue, SE | Washington, DC 20590 | 202-366-4000