Structural Concrete - Hassoun

932 Chapter 22 Prestressed Concrete Bridge Design
d. Compressive stress at the bottom of girder at the end of the section. Moment due to
self-weight is zero.
f ti = −F i
A g
− F i e end
− 0 = −1037
S tg S tg 713 + 1037(14.17) =−2.61 ksi > f
12715
ci_a
=−3.6ksi⇒ OK
7. Check Girder Stresses after Total Losses
Final Prestressing Force after total losses
f pf = 0.75f pu − Δf pT = 0.75(270)−38.5 = 167.5 ksi
Effective stress at transfer
F f = f pf A ps = 167.5(5.625) =942 K
a. Compressive stess at the top of girder at midspan due to effective stress and permanent
loads (Service I)
f tf = −F f
+ F f e m
− M DC1 + M DC2
− M DW + M LL
A g S tg S tg
S ic
= −942
713 + 942(27.59) 2045.6 + 255.6 350 + 2389.7
− − =−2.013 ksi > f
12,715 12,715 58,294
c1_a
=−3.6 ksi⇒ OK
b. Tensile stress at the bottom of girder at midspan due to effective stress and permanent loads
(Service III)
f bf = −F f
− F f e m
+ M DC1 + M DC2
+ M DW + 0.8M LL
A g S bg S bg
S bc
= −942
713 − 942(27.59) 2045.6 + 255.6 350 + 0.8(2389.7)
+ + = 0.37 ksi < f
12,224 12,224
17,407
tf_a
= 0.537 ksi ⇒ OK
c. Compressive stress at the top of deck due to added dead load and live load
f tc = −(M DW + M LL ) −(350 + 2389.7)
= =−0.91 > f
S tc 35,956
c_deck_a
=−2.4 ksi⇒ OK
Therefore, thirty-eight-0.5-in.-diameter low-relaxation strands satisfy service limit
state.
STRENGTH LIMIT STATE—FLEXURE IN POSITIVE MOMENT
Maximum factored moment for strength I is
M u = Strenght I = 7583 kip ⋅ ft
1. Find stress in prestressing steel-bonded tendons:
f ps = f pu
(
1 − k c d p
)