Page 206 - Bridge and Highway Structure Rehabilitation and Repair

CHAPTER 4 AN ANALYTICAL APPROACH TO FRACTURE AND FAILURE 181

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Mathcad or Excel spreadsheets. For precast concrete slab and beam bridges manufactured in
factory conditions, the lifting and erection weights can be extremely high, and biaxial bending

of beams and overhangs need consideration using finite element modeling.
For lifting and erection, the beam is non-composite and in some cases concrete has not
achieved its 28-day strength. Shear and bending strength would be much lower than for composite
action with the deck slab. Usually four lifting points are required. The criteria is to balance the
vertical shear forces at lifting points, and also the centroid of dead load and the lifting points
must coincide for stability.

4.17.2 Shear Design of Concrete Beams
A major revision to shear design deviating from the old Ritter-Morsch approach was recom-
mended by AASHTO LRFD code. The method has been incorporated in several computer software
programs such as PSLRFD prepared by PennDOT and will not be repeated here in detail.
The seven steps required as given below:
For values of parameters 0 versus v/fc1 (using plots of distribution of
x) and vs. v/fc1
(using plots of distribution of
x), refer to AASHTO Figure 5.8.3.4.2-1.
The LRFD code method is summarized as follows:

Step 1
Calculate M and V from elastic analysis

Calculate factored M and V u
u
Use load factors for strength I limit state
Dead load factor 3 1.25
Use with DC1 (deck slab DL) and DC2 (parapet DL)
Dead load factor for wearing surface 3 1.5 use with DW
Live load 4 Impact factor 3 1.75
Calculate V and M for 1.25(DC1 4 DC2) 4 1.5 DW 4 1.75 (LL+I)
u
u
a 3 A f /0.85 f1 b
s y c
Check if a : h f
Calculate maximum value of (lever arm) d
v
d 3 d 6 a/2, d is depth of beam (from top of deck to center line of rebar)
e
v
e
d 3 0.9 d or d 3 0.72 h (AASHTO Section 5.8.2.7)
v e v
Step 2
) 3 0.9, V 3 0
v p
v 3 V /) b d (AASHTO Section 5.8.3.4.2-1)
v
v
v
u
calculate v/f1 , V 3 0
c p
Step 3
Assume 0 3 40 deg. (AASHTO Section 5.8.3.4.2-2)
M /d + 0.5 V cot 0

3 u v u 0.002
x
EA
s s
Step 4
Use iterative process to calculate 0.
Using v/f1 and
, determine and 0 from AASHTO Fig. 5.8.3.4.2-1. If 0 is different from
c x
assumed value, use the new value of 0 and repeat.