Strut-and-tie modeling - Computational Analysis and Design of Bridge Structures - page 402

Load

(d) Behaves almost
elastically
until anticipated
failure load

Design 6(d)

1.0

Tie a

0.8

Severe
cracking 0.6

Design 6(a)

(c) Requires the largest
amount of plastic
deformation; thus it is more
likely to collapse before
reaching the failure load level

0.4

Tie b

Severe cracking
(extending to the whole
section at failure)

0.2

Design 6(c)

0.0 0.000

0.005 0.01 0.015

Displacement (under load)

Figure 13.3 Nonlinear finite element comparison of three possible models of a short
cantilever. (Data from MacGregor, J.G. et al., Reinforced Concrete: Mechanics
and Design , 5th Edition, Prentice Hall, Englewood Cliffs, NJ, 2008.)

• The crack pattern may also assist in selecting the best STM. It is suggested
by tests (MacGregor et al. 2008) that an STM developed with struts paral-
lel to the orientation of initial cracking will behave very well (Figure 13.4a).
• The minimum angle between a strut and a tie (Figure 13.4b) that are
joined at a node shall be 25° according to ACI (2002). There are sev-
eral other recommendations by other codes and researchers, but they
are all within close variation.
• Other than the empirical rules, the common constraints are the code
requirements. ACI and AASHTO code recommendations will also be
discussed.

Cracks

Concrete
compression

θ

ϕ cs

Reinforcement

(a) (b)

Figure 13.4 Strut. (a) Orientation of strut. (b) Angle at support. (Data from MacGregor,
J.G. et al., Reinforced Concrete: Mechanics and Design , 5th Edition, Prentice
Hall, Englewood Cliffs, NJ, 2008.)