Structural Concrete - Hassoun

486 Chapter 13 Footings
Let d be the larger of d 1 and d 2 .Ifd is less than d a (assumed), increase d a (or h) and
repeat. The required d should be close to the assumed d a (within 5% or 1 in. higher).
e. Check one-way shear (normally does not control in single footings):
i. V u11
= q u B(L∕2 − c∕2 − d) in the long direction (or for square footings):
V u11
d 11 =
2φλ √ f cB
′
ii. V u12
= q u L(B∕2 − c∕2 − d) in the short direction:
V u12
d 12 =
2φλ √ f cL
′
(for rectangular footings)
iii. Let d be the larger of d 11 and d 12 ; then use the larger d from steps iv and v.
iv. Determine h = (d + 4.5) in.; round to the nearest higher inch.
v. Calculate the final d = (h − 4.5) in.
f. Calculate the bending moment and the main steel in one direction only for square footings
and two directions for rectangular footings.
i. In the long direction (or for square footings)
( L
M uL = 0.5q u
2 − c ) 2
R
2
u = M uL
Bd 2
ii. In the short direction (for rectangular footings):
( B
M us = 0.5q u
2 − c ) 2
R
2
us = M us
Ld 2
iii. Calculate the reinforcement in the long direction, A sL , and in the short direction, A ss ,
using Eq. 13.14.
iv. Check that A sL and A ss are greater than the minimum steel reinforcement. Choose bars
and spacings. For square footings, the same bars are used in both directions. Distribute
bars in the bandwidth of rectangular columns according to Eq. 13.15.
g. Check bearing stress:
i. Calculate N 1 and
√
N 2 ∶ N 1 φ(0.85f cA ′ 1 ),whereφ is 0.65 and A 1 is the area of column
section; N 2 = N 1 A2 ∕A 1 ≤ 2N 1 ,whereA 2 is the square area of footing under column
(A 2 = B 2 ).
ii. If P u ≤ N 1 , bearing stress is adequate. Minimum area of dowels is 0.005A 1 . Choose
four bars to be placed at the four corners of the column section.
iii. If P u > N 1 , determine the excess load, P ex = (P u − N 1 ), and then calculate A sd (dowels)
= P ex /f y ; A sd must be equal to or greater than 0.005A 1 . Choose at least four dowel
bars.
iv. Determine the development length in compression for dowels in the column and in the
footing.
h. Calculate the development lengths, l d , of the main bars in the footings. The calculated l d
must be greater than or equal to l d provided in the footing. Provided l d = L/2 − c/2 − 3in.
in the long direction and l d = B/2 − c/2 − 3 in the short direction. Examples 13.2 and 13.3
explain these steps.