Reinforced Concrete Design II Lecture 13 Dr. Nader Okasha

Footing Design

Footing Introduction Footings are structural elements used to support columns and walls and transmit their loads to the underlying soil without exceeding its safe bearing capacity below the structure. Column Beam Loads Footing Soil M P L B

Footing Introduction The design of footings calls for the combined efforts of geotechnical and structural engineers. The geotechnical engineer, on one hand, conducts the site investigation and on the light of his findings, recommends the most suitable type of foundation and the allowable bearing capacity of the soil at the suggested foundation level. The structural engineer, on the other hand, determines the concrete dimensions and reinforcement details of the approved foundation

Types of Footing Isolated Footings Isolated or single footings are used to support single columns. This is one of the most economical types of footings and is used when columns are spaced at relatively long distances. P kN P L B C2 C1

Types of Footing Wall Footings Wall footing are used to support structural walls that carry loads for other floors or to support nonstructural walls. W kN/m W kN/m Wall Secondary reinft Footing Main reinft.

Types of Footing Combined Footings Combined footings are used when two columns are so close that single footings cannot be used. Or, when one column is located at or near a property line. In such a case, the load on the footing will be eccentric and hence this will result in uneven distribution of load to the supporting soil. P1 P2 P2 kN P1 kN L B C2 C2 C1 C1 L1 L2 L2

Types of Footing Combined Footings The shape of combined footing in plan shall be such that the centroid of the foundation plan coincides with the centroid of the loads in the two columns. Combined footings are either rectangular or trapezoidal. Rectangular footings are favored due to their simplicity in terms of design and construction. However, rectangular footings are not always practicable because of the limitations that may be imposed on its longitudinal projections beyond the two columns or the large difference that may exist between the magnitudes of the two column loads. Under these conditions, the provision of a trapezoidal footing is more economical.

Types of Footing Continuous Footings Continuous footings support a row of three or more columns P1 P2 P3 P4 P4 kN P3 kN P2 kN L P1 kN B

Types of Footing Strap (Cantilever ) footings Strap footings consists of two separate footings, one under each column, connected together by a beam called “strap beam”. The purpose of the strap beam is to prevent overturning of the eccentrically loaded footing. It is also used when the distance between this column and the nearest internal column is long that a combined footing will be too narrow. P2 kN P1 P2 Strap Beam property line P1 kN L1 L2 B1 C2 C2 B2 C1 C1

Types of Footing Mat (Raft) Footings Mat Footings consists of one footing usually placed under the entire building area. They are used when soil bearing capacity is low, column loads are heavy and differential settlement for single footings are very large or must be reduced. B L

Types of Footing Pile caps Pile caps are thick slabs used to tie a group of piles together to support and transmit column loads to the piles. P B L

Footing Distribution of Soil Pressure The distribution of soil pressure under a footing is a function of the type of soil, the relative rigidity of the soil and the footing, and the depth of foundation at level of contact between footing and soil For design purposes, it is common to assume the soil pressures are linearly distributed. The pressure distribution will be uniform if the centroid of the footing coincides with the resultant of the applied loads P L P L P L Centroidal axis Footing on sand Footing on clay Equivalent uniform distribution

Footing Pressure Distribution Below Footings The maximum intensity of loading at the base of a foundation which causes shear failure of soil is called ultimate bearing capacity of soil, denoted by qu. The allowable bearing capacity of soil is obtained by dividing the ultimate bearing capacity of soil by a factor of safety on the order of 2.50 to 3.0. The allowable soil pressure for soil may be either gross or net pressure permitted on the soil directly under the base of the footing. The gross pressure represents the total stress in the soil created by all the loads above the base of the footing. a net soil pressure is used instead of the gross pressure value P Df h

Footing Concentrically loaded Footings If the resultant of the loads acting at the base of the footing coincides with the centroid of the footing area, the footing is concentrically loaded and a uniform distribution of soil pressure is assumed in design, as shown in the figure Centroidal axis P L P/A B

Footing Eccentrically Loaded Footings Footings are often designed for both axial load and moment. Moment may be caused by lateral forces due to wind or earthquake, and by lateral soil pressures. Footing is eccentrically loaded if the supported column is not concentric with the footing area or if the column transmits at its juncture with the footing not only a vertical load but also a bending moment. P M P L P/A My/I y Centroidal axis e Centroidal axis y L P/A Pey/I

Footing Eccentrically Loaded Footings

Footing Eccentrically Loaded Footings 3

Footing Eccentrically Loaded Footings In this case, compressive stresses develop over the entire base of the footing

Footing Eccentrically Loaded Footings Large eccentricities cause tensile stresses on part of the base area of the footing. With the dimensions of the footing established and the eccentricity of the vertical load known, the distance between the resultant of the applied load P and the outside edge a can be established. The length of base on which the triangular distribution of soil pressure acts is equal to 3a, where a = L / 2 − e. Equating the resultant of the soil pressure to the applied forces gives

Eccentrically Loaded Footing Design

Eccentrically Loaded Footings Design Procedure Check service stresses to ensure pressure is all compressive under the footing 1.0 1.0 If tension stresses develop, resize the footing

Eccentrically Loaded Footings Design Procedure 1.2 1.6 F = 0.75 The critical section for punching shear is located at distance d / 2 from column faces and usually takes the shape of the column. Calculate Vu using the volume under the trapezoidal shaped stress distribution.

Eccentrically Loaded Footings Design Procedure The critical section for punching shear is located at distance d /2 from column faces and usually takes the shape of the column.

Eccentrically Loaded Footings Design Procedure l = 1.0 for normal weight concrete

Eccentrically Loaded Footings Design Procedure

Eccentrically Loaded Footings Design Procedure Calculate Mu using the volume under the trapezoidal shaped stress distribution.

Eccentrically Loaded Footings Design Procedure According to ACI Code 15.4.3, for square footings, the reinforcement is identical in both directions. For rectangular footings, the reinforcement in the long direction is uniformly distributed while the reinforcement in the short direction is concentrated in a band centered on centerline of column and with a width equals to the short dimension of the footing.

Eccentrically Loaded Footings Example 1

Eccentrically Loaded Footings Example 1 In order to have uniform soil pressure under the footing, the footing is to be positioned in such a way to balance the given moment through shifting the centroid of the footing 0.25 m away from the centroid of the column Continue the design as a concentrically loaded footing supporting only the axial loads transmitted by the column

Eccentrically Loaded Footings Example 2

Eccentrically Loaded Footings Example 2

Eccentrically Loaded Footings Example 2 Pu = 1.2PD + 1.6PL = 69 tons

Eccentrically Loaded Footings Example 2 Should use F as 0.75

Eccentrically Loaded Footings Example 2 Should use F as 0.75

Eccentrically Loaded Footings Example 2 Should use F as 0.75

Eccentrically Loaded Footings Example 2

Eccentrically Loaded Footings Example 2

Combined Footing Design

Combined Footings Design Procedure

Combined Footings Design Procedure

Combined Footings Example Design an appropriate footing/footings to support two columns A and B spaced at distance 2.1 m center-to-center. Column A is 20 cm × 30 cm and carries a dead load of 20 tons and a live load of 10 tons. Column B is 20 cm × 40 cm in cross section but carries a dead load of 30 tons and a live load of 15 tons. Width of footing is not to exceed 1.0 m, and there is no property line restriction.

Combined Footings Example

Combined Footings R Pb Example Pa 2.1 m l1 x1 x2 l2

Combined Footings Example Should use 1.2D+ 1.6L

Combined Footings Example

Combined Footings Example

Combined Footings Example

Combined Footings Example

Combined Footings Example

Combined Footings Example