318M-19: Building Code Requirements for Concrete and Commentary The design of wall footing, which is also termed as strip footing, is based on the principles of beam action with only slight modifications.
Wall footing should be designed to safely support structural or nonstructural walls and transmit and distribute the loads to the soil in such a manner that the load-bearing capacity of the soil is not surpassed. In addition to avoiding excessive settlement and rotation and maintain sufficient safety against sliding and overturning.
Wall footing runs along the direction of the wall. The size of the footing and the thickness of the foundation wall are specified on the basis of the type of soil at the site and loading conditions. Reinforcement area and distribution is carried out based on the requirements of ACI 319-19 (Building Code Requirements for Structural Concrete.
Analysis of Wall Footing
The simple principles of beam action apply to wall footings with only minor modifications. Fig. 1 shows a wall footing with the forces acting on it. If bending moments were computed from these forces, the maximum moment would be found to occur at the middle of the width.
Actually, the very large rigidity of the wall modifies this situation, it is satisfactory to compute the moment at the face of the wall section 1-1. Tension cracks formed under the face of the wall rather than in the middle.
For footings supporting masonry walls, the maximum moment is computed midway between the middle and the face of the wall, because masonry is less rigid than concrete. The maximum bending moment (Mu) in footings under concrete walls is computed using equation 1.
Where:
qu: ultimate bearing capacity of soil under wall footing which is equal to the ultimate distributed load divided by required area of footing.
b: width of wall footing .
a: width of the wall supported by wall footing.
The vertical shear force (Vu) can be calculated on section 2-2 located at distance d from the face of the wall. Equation 2 can be used to compute shear force. Development length calculation is based on the section of maximum moment (section 1-1).
Where:
d: distance between wall face and location of vertical shear force application and it is equal to the effective depth of the wall footing section.
Footing size
Footing sizes are determined for unfactored loads and effective soil pressure (qe) which is computed from allowable bearing pressure (qa). The reason of using unfactored loads is that, for footing design, the safety is provided by overall safety factors.
The allowable bearing pressure is established based on principle of soil mechanics, on the basis of load tests, and other experimental determinations. The allowable bearing pressure under service loads is computed using safety factor of 2.5 to 3. This safety factor would prevent the exceedance of bearing capacity of soil and keep its settlement within tolerable limit.
The area of footing (Areq) is determined by total of service loads divided by allowable bearing pressure using equation 3.
Where
D: dead load on footing .
L: live load on footing.
qe: effective bearing pressure which is equal to allowable bearing capacity-(weight of fill+weight of concrete)
If other loads such as wind loads and seismic loads are present, then equation 4 should also be used compute area of footing. The larger value of these two equations are considered to be the area of footing.
Where:
w: equal to 1.3 if wind load is computed based on ASCE, otherwise it would be equal to 1.
W: wind load
E: seismic forces
The width of wall footing is computed from the required area. The length of the of the footing is taken as 1m.
Footing Depth
According to ACI 318-19 section 13.3.1.2,overall depth of foundation shall be selected such that the effective depth of bottom reinforcement is at least 150 mm.
In sloped, stepped, or tapered foundations, depth and location of steps or angle of slope shall be such that design requirements are satisfied at every section.
Calculate Reinforcement Areas
Main reinforcement
The main reinforcement area is computed using the following expression.
Where:
As: main reinforcement area
Mu: ultimate moment taken from equation 1.
Phi: strength reduction factor which is equal to 0.9.
fy: yield strength of steel.
d: effective depth, take concrete cover of 75mm.
a: depth of rectangular stress block.
The depth of rectangular stress block is assumed in equation 5. Then, steel area is computed by trial and error. Three trials are recommended, and it is advised to take (0.2xfooting depth) as first trial for a.
Minimum Reinforcement
The minimum Reinforcement is computed using the following expressions:
For steel grade of less than 420:
For steel grade of 420:
Where:
b: width of footing
h: depth of footing
Distributed reinforcement area is equal to the value of equation 7. So, this value is the distributed reinforcement for the wall footing.
Bar Spacing/ Placement
The reinforcement area computed from equation 5 is divided by area of one bar (Ab) to estimate number of bars (n). Then, number of bars area used to compute spacing for main reinforcement using the following expression
Main bar spacing:
Distributed bar spacing:
Number of distributed bar is equal to the area of steel from equation 7 divided by area of one bar to be used for distributed reinforcement. Then, spacing is computed by dividing width of the footing by number of distributed bar.
Maximum Spacing:
Maximum spacing is the smallest of 3h or 450mm. so, steel bar spacing should not be greater than this value.
Shear Strength of Concrete
Design shear strength of concrete should be equal or greater than ultimate shear force computed from equation 2 otherwise the depth of the footing should be increased. The shear strength of concrete is calculated as follow:
Where:
Vc: concrete shear strength
Phi: strength reduction factor which is equal to 0.75.
Lamda: equal to 1 for normal strength concrete.
fc': concrete compressive strength which should not be less than 17MPa.
b: width of the footing.
d: effective depth of footing.
Summery of Design Procedure
- Estimate footing thickness (h) which should meet shear requirement and provide minimum effective depth of 150mm.
- Compute weight of fill and weigh of footing.
- Calculate effective bearing capacity, qe.
- Estimate required area, Areq
- Calculate design pressure (qu) on the base of footing (Areq) due to factored loads.
- Compute shear force and design shear strength of concrete to check shear requirements.
- Calculate maximum moment and then reinforcement area.
- Compute minimum reinforcement and maximum spacing.
- Estimate main and distributed bars spacing.
- Draw design draft.
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