 Hello, I am Dr. Siddish Kumar Kashid, Professor in Civil Engineering, Valshan Institute of Technology, Solapur. I am presenting geotechnical design of a rectangular combined footing. At the end of this session, students will be able to elaborate suitability of rectangular combined footings and students will be able to proportion a rectangular combined footing. The proportioning is expected, not the RCC design. Now, let us discuss the suitability of combined footing. When two columns are close together, causing overlap of adjacent acerated footings, in that case combined footing will be suitable. When soil bearing capacity is low, which causes overlap of adjacent acerated footings if designed, in such cases also we need to go for a combined footing. When proximity of building line or existing building or sewer adjusting to building column is there, then also we need to go for a combined footing. The combined footing may be rectangular trapezoidal or T-shaped in plan. The geometric proportions and shapes are so fixed that the centroid of a footing area coincides with the resultant of column loads, it is very important. Rectangular footing is provided when loads on columns are nearly equal and rectangular footing is also provided when one of the projections of footing is restricted or width of footing is restricted, whereas we go for trapezoidal footing when one column load is much more heavier than the other load. Let us see the combined footings. So this is a rectangular combined footing of slab type. This is the top view. This is section. This is slab and beam type combined footing which is rectangular. This is one special type that is a strap type footing. In 3D we can observe this is a rectangular combined footing. These are the columns and this is the footing. These are columns in plan and this is the footing in plan. One can also go for trapezoidal footing which is seen as it is shown here in this figure. A completely cast rectangular combined footing can be seen here. These two columns are quite near to each other and combined footing is provided to these two columns which is rectangular in shape. Now let us discuss about the conventional method of design assumptions. The footing or mat is infinitely rigid. The deflection of footing does not influence the pressure distribution below the footing. The soil pressure is distributed in a straight line or a plain surface. The centroid of soil pressure coincides with the line of action of resultant force of all the loads acting on the foundation. So while proportioning this footing we need to have these assumptions which are very important to have the uniform distribution of load all over the footing. Now what is expected? Now here this is column 1 carrying load P1. Here there is column C2 carrying load P2. Now resultant of these two forces will be this R. Now the distance between P1 and R let it be L1 and distance between P2 and R let it be L2. Now when the loads are slightly different the resultant will always shift towards the heavier load. So if this load is heavier it will shift towards light. This load is lighter and this is heavier this will shift towards left. But ultimately what we have to see is that we need to find resultant of these two going in this way and this resultant of these two forces has to cut the footing at half of its length L by 2 and L by 2. So that there will be uniform distribution ultimately below the footing. So this is the basic idea. These projections can be different depending upon the heavy or light loads. Let us discuss one example which will clarify the concepts. A combined footing has to be proportioned for two columns C1 and C2 carrying loads P1 as 1200 kilo Newton and P2 as 1000 kilo Newton. So this is load 1200 kilo Newton on column C1. There is another load 1000 kilo Newton on C2. The net allowable pressure on soil is 250 kilo Newton per meter square. The center to center distance between the columns is 5 meter. The footing should not extend beyond 0.5 meters beyond face of any column. That is the another condition which is given to us. Now let us discuss what is given. Column size 130 centimeter by 50 centimeter, column size 230 centimeter by 50 centimeter that is 0.3 meter by 0.5 meter, load P1 1200, load P2 1000 kilo Newton, allowable bearing capacity 250 kilo Newton per meter square. For uniform stress at bottom of the footing resultant should be at middle of length of footing that we have to see. So let us go for calculations. We know that this allowable bearing capacity value of 250 kilo Newton per square meter should not be crossed. Accordingly we need to provide area of footing. So working load divided by area of footing has to be equated with allowable bearing capacity. We know the working load 1200 plus 1000. We also know the allowable bearing capacity 250 kilo Newton per meter square. So accordingly we need to calculate the required area of footing. So solving this we get the area of footing as 8.80 square meter. Now we know that the footing being rectangular area of footing is breadth of footing into length of footing and that is to be equated to 8.80 square meter. Now here center to center distance between columns is 5 meter and CG has to match with the line of fraction of the resultant force. So let us see. So resultant R is 1200 plus 1000 that is 2200 kilo Newton taking moments about center of column 1. It means this is our column 1 and we are taking moments about this center of column 1. So when we take the moments 2200 into L1 that is to be matched with 1200 into 0 that is the moment of the force passing through column 7 and this is the moment of a force passing through column C 2 which is at 5 meter distance and that algebraic sum of moments of these two forces is compared and equalized with the moment of the resultant. So when we solve this we get L1 is equal to 2.272 meter. What we do? 5 minus 2.272 that is 2.728 that is L2. What is L2? So this is the distance L2 in this way. We calculated L1 and L2. Now distance of centroid of footing shall lie at L by 2 capital L by 2 here L is the length of footing. So that can be calculated by a projection beyond column width half the column width plus L1. So projection allowed for column 1 is 0.5 meter which is the maximum projection allowed plus half the column width is 0.25 plus L1 is 2.272 that is 3.022 so it means exact half length of footing is 3.022. So the full length of footing will be just two times this that is 2 into L by 2 that is 2 into 3.022 that is 6.044 meter. So once we got the length of footing and once we know the area of footing then let us calculate the width. So area by length of footing will be the breadth of the combined footing. So 8.80 divided by 6.044 that is 1.455 meter is required width of footing. So provide length of footing as 6.044 meter and width of footing as 1.455 meter as shown in figure and footing will be in this way. So you will find that though one of the loads is heavier and one of the loads is lighter still we have adjusted this footing in such a way by adjusting the projection here that the resultant is exist exactly at the mid of this particular length. So here we find slightly more projection here we find lesser projection but it does not matter because ultimately the resultant is at the middle of the length and middle of the width distributing the pressure evenly on the footing and the soil. Now let us take some questions if the resultant of soil pressure coincides with the resultant of loads the soil pressure is assumed to be non-uniform uniformly distributed zero none of the mission. So naturally it has to be uniformly distributed when two column loads are nearly equal which of the possible footing can be provided strap raft rectangular mat of course when the loads are nearly equal it has to be a rectangular combined footing. For a rectangular combined footing X bar is given by L by 2 L by 3 less than X bar less than L by 2 X bar is equal to L by 3 and none of the mentioned. Actually the footing being rectangular combined footing the X bar is L by 2 it means at half the mid width the resultant has to pass these are the references used for this presentation. Thank you.