Strut-and-tie modeling - Computational Analysis and Design of Bridge Structures - page 411

145 kip (typ.)

O

P N

Q R M

G

F E

J K L

190 kip 190 kip

Force in strut
= 239 kip

H

I D

190 kip 190 kip

Force in strut
= 305 kip

A

B

C

145 kip (typ.)

(c)

Figure 13.10 (Continued) (c) 3D STM truss resulting from the flow of forces and resulting
member forces. (Data from Martin Jr., B.T. and Sanders, D.H., “Analysis and Design of
Hammerhead Pier Using Strut and Tie Method,” Final Report-Project 20-07_Task 217,
National Cooperative Highway Research Program, Transportation Research Board,
Washington, DC, November, 2007.)

( f y = 413.7 MPa). The original reinforcement was determined by checking
the moment capacity at the face of the column as well as one-way and two-
way shear at the critical sections.
Assume typical load for each nine-load location is from the factored load-
ing 574 kN (= 5164 kN/9) plus load based on moment 71 kN (the moment
divided by the section modulus of the pile group, 521/7.3 = 71 kN or
384/24 = 16 kip) for a total of 645 kN (145 kip) (see Figure 13.10b and c).

13.2.2.1 Check the capacity of the ties
The required area of reinforcement ( A st ), is

P
f

190
0 9 60

u
y

2 2

A = = = 3 52 . in ( 2270 96 . mm )

st

φ . ×

The factored flexural resistance required to resist 1.2 M cr

bh

2

12 11 36
6

2

× ×

′

M ≥ 1 2 . × 0 36 . f = 1 2 . × 0 36 3 . = 21 334 , kip-in

cr c

6

= 1778 kip-ft( 2412 34 . kN-m)

The minimum area of flexural reinforcement corresponding to 1.2 M cr can
then be determined.