Structural Concrete - Hassoun

306 Chapter 8 Design of Deep Beams by the Strut-and-Tie Method
P
D
18"
P D = 300 K
P L = 240 K
6'
A
1.5'
6' 6'
1.5'
B
Figure 8.12 Example 8.1.
2. Check if the beam is deep according to to the ACI Code, Section 9.9. clear span, l n = 12 ft, h = 6ft,
and l n /h = 2 ≤ 4, deep beam.
3. Calculate the maximum shear strength of the beam cross section. Let V u at A = R A = 384 K and
assume d = 0.9h = 0.9 × 72 = 64 in.:
V n = 10 √ √
f c ′ b w d = 10 4000(18 × 64) =728.6K
φV n = 0.75(728.6) =546 K > V u
4. Select a truss model. A triangular truss model is chosen. Assume that the nodes act at the centerline
of the supports and at 6.0 in. from the lower or upper edge of the beam (Fig. 8.13). The strut-and-tie
model consists of a tie AB and two struts AD and BD. Also, the reactions at A and B and the load
P u at D represent vertical struts:
√
Length of diagonal strut AD = 60 2 + 81 2 = 100.8in.
Let θ be the angle between the strut and the tie. Then tan θ = 60/81 = 0.7407 and
θ = 36.5 ∘ > 25 ∘ , OK (ACI Section 23.2.7).
5. Calculate the forces in the truss members:
( ) 100.8
Compression force in strut AD: F AD = F BD = 384 = 645 K
60
( ) 81
Tension force in tie AB: F AB = 645 = 518.3K
100.8
6. Calculate the effective strength f ce . Assume that confining reinforcement is provided to resist
the splitting forces. Struts AD and BD represent the bottle-shaped compression members, and
therefore β s = 0.75, and
OK
f ce = 0.85β s f c ′ = 0.85 × 0.75 × 4 = 2.55 ksi