Page 179 - Bridge and Highway Structure Rehabilitation and Repair

154 SECTION 2 STRENGTHENING AND REPAIR WORK

For permit loads and HS-25 trucks or tandem trucks, slab thickness will be governed by
punching shear, and thickness used should be adequate. Reinforcing bars should be designed
for bending moments from FEM analysis. Usually bending shear is not a problem for large
width slabs.
• Comparison of analysis of approach slab on grade using differential equations and fi nite
element methods
• Exposed pile analysis using L-pile or COMP624P program
• Fatigue analysis for category B

• Sheet piling analysis
• Location of section for maximum BM
In structural analysis applied to the bridge framework of composite slab-beam girders with
substructures, many assumptions are made. The mathematical model used is as accurate as the
validity of the assumptions. Effects of some assumptions are addressed here.

4.9.4 Shape Effects for Steel or Aluminum Sign Structures
Sign structures with hollow tubes: Selection of closed hollow tubular sections rather than
open sections is recommended for resisting torsion. Members’ torsional capacity is evaluated
and can be used for primary design. Three thickness ranges are considered:
If r 3 Internal radius, r 3 External radius,
1 2
r 3 Radius of solid shaft of equivalent area, identical unit weight and maximum stress
T 3 ! r /2
3
solid
4
4
T hollow 3 ( !/2) (r 6 r )/r 1
2
1
4
Equating maximum stress, T /T 3 (r 6 r )/r r 3 (4.16)
4
hollow solid 1 2 1
2
2
2
Equating areas, (!/2) r 3 (!/2) (r 6 r )
1
2
T /T 3 (r 4 r )/r r
2
4
hollow solid 1 2 1
2
3 r /r (1 4 1/n ), if r /r 3 n (4.17a)
1
2
1
2
Also r 3 r 6 (r /n) 2
2
1 1
2
r /r 3 n/ (n 6 1)
1
2
T /T 3 (n 4 1)/[n (n 6 1)]; (4.17b)
2
hollow solid
n 3 1.25, T hollow /T solid 3 2.563/ (1.25 8 0.75) 3 2.734
n 3 1.1, T /T 3 2.21/1.1 8 0.458 3 4.384
hollow solid
A hollow beam can carry 4.384 times greater torsion than an equivalent solid beam of the
same weight and is ideal for members subjected to torsion.
4.9.5 Initially Curved Shallow Beams with Camber (Linear Strain)
It is common practice to design beams with upwards camber to negate dead load defl ection.
Camber introduces compressive stress in bottom flange especially at midspan. This simple ap-

proach has advantages similar to prestressing to introduce compression. Net deflection in practice

will be due to live load only. An initially vertical curved beam is used. However, the effect of
camber or initial curvature needs to be considered in analysis as follows:
If the depth of the cross section is small compared to the radius of the curvature, stress dis-
tribution is linear (Figure 4.9). This is the case for most of the beams used in practice. However,
for deep beams with initial camber stress, distribution will be non-linear (Figure 4.10).