DESIGN OF FOOTINGS – IS-456 RECOMMENDATIONS:GENERAL
1. In sloped or stepped footings, the effective cross – section in compression shall be limited by the area above the neutral plane, and the angle of slope or depth and location of steps shall be such that the design requirements are satisfied at every section. Sloped and stepped footings that are designed as a unit shall be constructed to assure action as a unit.
2. Thickness at the edge of footing: In reinforced and plain concrete footings, the thickness at edge shall be not less than 150 mm for footings on soils nor less than 300mm above the tops of files for footing on piles.
3. In the case of plain concrete pedestals, the angle between plane passing through the bottom edge of the pedestal and the corresponding junction edge of the column with pedestal and the horizontal plane (fig.1) shall be governed by the expression
Where = calculated maximum bearing pressure at the base of the pedestal in = characteristic strength of concrete at 28 days in .
MOMENTS AND FORCES
1. In the case of footings on piles, computation for moments and shears may be based on assumption that the reaction from any pile is concentrated at the centre of the pile.
2. For the purpose of computing stress in footings which support a round or octagonal concrete column or pedestal, the face of the column or pedestal shall be taken as the side of a square inscribed within the perimeter of the round or octagonal column or pedestal.
3. Bending Moment:
i. The bending moment at any section shall be determined by passing through the section a vertical plane which extends completely across the footing and computing the moment of the forces acting over the entire area of the footing on one side of the said plane.
ii. The greatest bending moment to be used in design of an isolated concrete footing which supports a column, pedestal or wall, shall be the moment computed in the manner prescribed in (i) at section located as follows:
a. At the face of the column, pedestal or wall, for footings supporting a concrete column, pedestal or wall.
b. Half way between the center line and the edge of the wall, for footings under masonry walls, and
c. Half way between the face of the column or pedestal and the edge of the gusseted base, for footing under gusseted bases.
4. Shear and Bond
i. The shear strength of footings is governed by the more severe of the following two conditions:
a. The footings acting essentially as a wide beam, with a potential diagonal crack extending in a plane across the entire width, the critical section for this condition shall be assumed as a vertical section located from the face of the column, pedestal or wall at a distance equal to the effective depth of the footing in case of footings on soils and a distance equal to half the effective depth of footing for footing on piles.
b. Two way action of the footing, with potential diagonal cracking along the surface of truncated cone or pyramid around the concentrated load: in this case, the footing shall be designed for shear in accordance with appropriate provisions discussed below. (Fig.2)
Fig.2 – Critical Section for Shear
ii. In computing the external shear on any section through a footing supported on piles, the entire reaction from any pile of diameter whose centre is located /2 or more outside the section shall be assumed as producing shear on the section: the reaction from any pile whose centre is located /2 or more inside the section shall be assumed as producing no shear on the section. For intermediate portions of the pie centre, the portion of the pile reaction to be assumed as producing shear on the section shall be based on straight line interpolation between full value at /2 outside the section and zero value at /2 inside the section.
iii. The critical section for checking the development length in a footing shall be assumed at the same planes as described for bending moment in B(3) and also at all other vertical planes where abrupt changes of section occur. If the reinforcement is curtailed, the anchorage requirements should be checked.
iv. Thus according to the above provision, shear stress is to be checked for (i) one way action (i.e. beam shear) for which the governing section AB is at a distance d from the face of column or pedestal (fig.2(a)) and (ii) two way shear (i.e. punching shear), for which the governing section is along the perimeter ABCD situated at a distance d/2 from the face of the column or pedestal (fig.2(b)).
For the two way action, the calculated shear stress should satisfy the following relation
Where but not greater than 1.0
Where b= short side of column, a= long side of column.
in limit state design
= net shear force acting on the perimeter
For the beam shear, the nominal shear stress across AB should satisfy the relation
Where = the permissible shear stress for the grade of the concrete, corresponding to the reinforcement.
K= factor for slabs.
The total tensile reinforcement at any section shall provide a moment of resistance at least equal to the bending moment on the section calculated in accordance with B(3). Total tensile reinforcement shall be distributed across the corresponding resisting section as given below:
i. In one way reinforced footing, the reinforcement shall be distributed uniformly across the full width of the footing.
ii. In two way reinforced square footing, the reinforcement extending in each direction shall be distributed uniformly across the full width of the footing.
iii. In two way reinforced rectangular footing, the reinforcement in long direction shall be distributed uniformly across the full width of the footing. For reinforcement in short direction, a central band equal to the width of the footing shall be marked along the length of the footing and portion of the reinforcement determined in accordance with the equation given below shall be uniformly distributed across the central band.
Where is the ratio of the long side to the short side of the footing.
The remainder of the reinforcement shall be uniformly distributed in the outer potions of the footing.
TRANSFER OF LOAD AT THE BASE OF COLUMN
The compressive stress in concrete at the base of the column or pedestal shall be considered as being transferred by bearing to the top of the supporting pedestal or footing. The bearing pressure () on the loaded area shall not exceed the permissible bearing stress in direction compression multiplied by a value equal to but not greater than 2.
Where = supporting are for bearing of footing, which in sloped or stepped footing may be taken as the area of the lower base of the largest frustrum of a pyramid or cone contained wholly within the footing and having for its upper base, the area actually loaded and having side slope of one vertical to two horizontal and
= loaded area at the column base.
For limit state method of design , the permissible bearing stress shall be .
The actual bearing pressure = column load divided by the area of column at the base.
Thus, where ‘a’ and ‘b’ are the sides of the column.
1. Where the permissible bearing stress on the concrete in the supporting or supported member would be exceeded, reinforcement shall be provided for developing excess force, either by extending the longitudinal bars into the supporting members or by dowels (see 3 below).
2. Where transfer of force is accomplished by reinforcement, the development length of the reinforcement shall be sufficient to transfer the compression or tension to the supporting member.
3. Extended longitudinal reinforcement or dowels of at least 0.5 percent of the cross sectional area of the supported column or pedestal and a maximum of four bars shall be provided. Where the dowels are used, their diameter shall not exceed the diameter of the column bars by more than 3mm.
4. Column bars of diameter lager than 36 mm, in compression only can be dowelled at the footings with bars of smaller size of the necessary area. The dowel shall extend into the column, a distance equal to the development length of the column bar and into the footing, a distance equal to the development length of the dowel.
For footings, minimum nominal cover shall be 50mm.
The nominal reinforcement for concrete sections of thickness greater than 1m shall be 360 per meter length in each direction on each face. This provision does not supercede the requirement of minimum tensile reinforcement based on the depth of the section.