Structural Concrete - Hassoun

8.6 Deep Members 315
2. Check if beam is deep. Height of beam (h) is 4 ft, clear span (l n )is4ft.
l n
h = 4 2 = 2 < 4ft
(Entire beam is in D − region)
3. Calculate maximum shear strength of the beam cross section. Let V u at A be given as R A = 125 K
and assume
d = 0.9h = 0.9 × 48 = 43.2in., use 43 in.
φV n = φ(10) √ √
f c ′ b w d = 0.75(10) 4000(12)(43) =244 K > V u = 125 K (OK)
4. Select a truss model. A triangular truss model is chosen. Assume that nodes act at the centerline
of the supports and 4 in. from the lower and upper edges of the beam. The strut-and-tie model
consists of a tie, BC, and two struts AB and AC.
Let the angle between the strut and tie be θ = 60 ∘ > 25 ∘ OK.
5. Calculate the forces in truss members.
At the joint A (C–C–C) nodes:
250 K
F AB F AC
F AB = F AC
At joint B (C–C–T) nodes:
F AB cos 30 ∘ = 250 K
F AB = 250
cos 30 ∘ = 144.34 K
144.34 K
F BC
125 K
F BC = 144.34 cos 60 = 72.17 K
6. Check size of bearing:
Effective strength of node A (C–C–C node) =0.85f c ′ φ
Effective strength of node B, C (C–C–T node) =0.75f c ′
P φ
Bearing area required at node A = u
0.85f c ′ φ = 250
0.85 × 4 × 0.7 = 105in.2
Bearing area required at nodes B and C =
0.85f c ′ φ = 125
0.75 × 4 × 0.7 = 60in.2
Bearing area proposed = 8 ′′ × 8 ′′ = 64 in. 2 < 105 in. 2 (not safe)
Since the width of beam is 12 ′′ , keep a “width with clear spacing 1.5” on both sides. The
bearing pad length L is
L = 105
9 = 11.67′′
Use 9 ′′ × 12 ′′ bearing pad at the load position and 8 ′′ × 8 ′′ bearing pad at support.
P u