Page 303 - Bridge and Highway Structure Rehabilitation and Repair

278 SECTION 2 STRENGTHENING AND REPAIR WORK

Total nominal shear resistance V 3 V 4 V s
n
c
v 3 (V 6) V ) / ) b d LRFD Eq (5-65)
u
v
v
p
v/fc1 0.25

At first critical section for shear, calculate design (factored) dead load and live load mo-
ments.

Using the LRFD shear design flow chart and Table 1 (LRFD 5.8.3.4.2), LRFD Table 5-5,
and Figure 5-19, calculate ε :
x
ε 3 [M /d 4 0.5 N 4 0.5 (V 6 V ) cot 06 A f ] / 2 (Es A 4 E A ) LRFD Eq. (5-70)
x
p
ps p0
s
p
v
u
u
u
ps
0.002 (LRFD 5.8.3.4.2)
Calculate V 3 V 4 V and compare with the simplifi ed method.
n
c
s
12. Check longitudinal reinforcement LRFD 5.8.3.5
Force T 3 [M / ) d 4 0.5 N / )4 (V / )6 0.5 V 6 V ) cot 0] LRFD Eq. (5-74)
u
u
v
s
u
p
Development length L 3 (f 6 ⁄3 f ) d LRFD Eq. (5-36)
2
d
ps
b
pc
13. Compute nominal shear resistance at stirrup change (at 20 ft. from center line of bearing)
(LRFD 5.11.4)
Compute maximum shear at stirrup change.
Check longitudinal reinforcement.

Check tensile capacity on flexural tension side of member 9 Force T.
14. Load rating equation
RF 3 [C 6 ( ) (DC) 6 ( ) (DW) ? (P)] / (LL 4 IM) (EQ 6-1)
L
DC
P
DW
Condition factor () ) 3 1.0 for no deterioration. (LRFD 6.4.2.3)
c
System factor () ) 3 1.0 for a multi-girder bridge. (LRFD 6.4.2.4)
s

Resistance factor ()) 3 1.0 for flexure (LRFD 5.5.4.2.1)
Design rating equation LRFD 6.4.3
Strength I limit state:
C 3 () ) () ) ()) R n
c
s
RF 3 [() ) () ) ()) R 6 ( ) (DC) 6 ( ) (DW)] / (LL 4 IM) (LRFD 6.5.4.1)
c
DW
L
DC
s
n
Condition factor () ) 3 1.0 for no deterioration. (LRFD 6.4.2.3)
c
System factor () ) 3 1.0 for a slab bridge (LRFD 6.4.2.4)
s
Factors for inventory rating: 3 1.25; 3 1.5; 3 1.75
DC
LI
DW
Factors for operating rating: 3 1.25; 3 1.5; 3 1.35
DC
DW
LL
Flexure at midspan: Operating rating 3 Inventory rating 8 ( / )
LO
LI
A systematic evaluation of the shear and longitudinal yield criteria based on shear-moment
interaction should be performed along the length of the beam at L/20, in addition to points
of special interest. Flexural ratings should be checked at maximum moment sections and at
sections where there are changes in fl exural resistance.
15. Service III limit state
Rating factor for inventory level
f 3 Compressive stress due to effective prestress
pb
Allowable tensile stress 3 0.19 (fc1) (LRFD 5.9.4.2.2)
0.5
Flexural resistance f 3 f 4 Allowable tensile stress
R
pb
Compute dead load stresses f D
Compute live load stresses f LL 4 IM
RF 3 [(f 6 ( ) f ] / f (LRFD 6.5.4.1)
D
D
R
L LL 4 IM