 Hello, I am Dr. Siddish Kumar Kashi, Professor in Civil Engineering, Valchan Institute of Technology, Sulapu. I am presenting a topic geotechnical design of a trapezoidal combined footing. Learning outcomes of the session. At the end of the session, students will be able to describe trapezoidal combined footing. They will be able to state the situations in which trapezoidal combined footing is adopted and they will be able to design the shape and size of trapezoidal combined footing depending upon load and safe bearing capacity of the soil. Let us see here combined footings. Combined footings can be rectangular combined footing or trapezoidal combined footing. This is a 3D view. This is a plan for a rectangular combined footing. This is a 3D view and this is a plan of a trapezoidal combined footing. Combined footings we provide when two columns are quite close together and which may cause overlap if isolated footings are designed. Combined footings are also adopted when soil bearing capacity is low and which may cause overlap of adjacent isolated footings if designed. Then there is a proximity of building line or existing building or sewer adjusting to building column. In such cases also we need to adopt combined footing. If a rectangular combined footing cannot provide assumed uniform contact pressure, we go for trapezoidal combined footing. Also if the column carrying much larger load has too limited space for split footing then also we may go for trapezoidal combined footing. In such case the resultant of all column loads including moments will be much closer to the heavier column. Now let us see a typical trapezoidal combined footing. The footing has trapezoidal shape with smaller side B1, longer side B2. Length of the footing is L, this is column C1, this is column C2. The distance in between centers of column we call it as L dash. This is a point which is centroid of a trapezoidal combined footing at distance x dash from C2 and it is at the sense x bar from the side B2. Now here this is a special type of trapezoidal footing with both columns are facing with the boundary. Resultant of two forces carried by column C1 and column 2 will ultimately drop here at the centroid. Let us discuss the design steps. Design steps for proportioning the column footing. Firstly locate the point of application of column loads on the trapezoidal footing. Then proportion the footing in such a way that the resultant of loads passes through centroid of trapezoidal footing and then compute the area of footing depending upon allowable soil pressures. Now let us see how we proportion the trapezoidal footing. So let B1 be small side, B2 be long side of this trapezoidal footing, L is the length as shown in this way. So as it is a trapezoid we know area of trapezoidal is given by A is equal to B1 plus B2 divided by 2 that is average of these two sides multiplied by L. One more formula is for the x dash, x dash it means this distance x dash. The centroid of a trapezoid lies at distance x dash from the side B2. It is going to lie on this L by 3 plus 2 times B1 this B1 plus B2 divided by B1 plus B2. It means here we have established the position of centroid by this formula. Now how to proportion the footing? In order to obtain uniform contact pressure the location of centroid of footing must be adjusted to agree with the location of resultant load. The resultant load means the resultant of loads coming on column 1 and column 2. Using known values of the base area A and L one can decide sides B1 and B2. Let us see this by example a trapezoidal footing is to be provided to support two square columns of size column C1 0.5 meter by 0.5 meter, column C2 0.3 meter by 0.3 meter. The columns are 6 meter apart face to face. The safe bearing capacity is 400 kilo Newton per square meter. Column C1 carries total load of 5000 kilo Newton and column C2 carries total load of 3000 kilo Newton. These two loads include the dead loads. Then you are asked to design a suitable size of trapezoidal footing so that footing does not extend beyond columns touching the boundary line. We are given that safe bearing capacity of soil is 400 kilo Newton per square meter and column faces are to match with the boundary. Hence length L of footing would be 6.4 plus 0.5 by 2 plus 0.3 by 2 half the width of heavy column and this is half the width of the lighter column it means carrying lighter loads so that is 6.8 meter. Now we have formula safe bearing capacity is equal to working load divided by area of footing two columns are carrying working load of 5000 plus 3000 that is 8000. So this 8000 divided by area of footing is equal to the safe bearing capacity. So when we solve this we get the area of footing as 20 square meter. Now we also know that the formula for area of footing as it is trapezoidal it is side b1 plus side b2 divided by 2 into length of footing that is 20 meter. Length is 6.8 meter as it is restricted by the position of columns. So keeping this L here we get b1 plus b2 as 5.882 meter this is equation one. Let us go for another equation which is given by the moments of forces about center of one of the columns. We know that magnitude of resultant force is 5000 plus 3000 that is 8000 kilo Newton. So resultant force is 8000 kilo Newton finding line of action of the resultant load or resultant force. We know that the algebraic sum of moments of these two column forces has to be matched with the moment of resultant force. So 3000 into 6.4 that is the moment of one of the forces plus 5000 into 0 the lever arm is 0 because the force passes through the same point about which we are taking the moments. So resultant into x dash is equal to this quantity after solving we get x dash as 2.4 meter. So when x dash is 2.4 meter means this is x dash that is 2.4 meter in which you need to add this much that is 0.5 by 2. So when we multiply it by say 0.5 multiplied by 0.5 that is 0.5 by 2 that is 0.25. So 2.4 plus 0.25 we get x bar is equal to 2.65. So x bar is 2.65 meter it shall also match with the centroid of trapezoidal footing hence x bar that is equal to 2.65 that is also equal to L by 3 into b1 plus 2 b2 divided by b1 plus b2 it means this formula of locating a centroid of a trapezoidal footing. So putting these values one relation we get in terms of b1 b2. So b1 plus 2 b2 divided by b1 plus b2 we get 1.169 we also had a equation b1 plus b2 is equal to 5.882. So we solve these two equations and ultimately we get b1 is equal to 4.889 meter and b2 is equal to 0.994 meter and length L of footing is 6.8 meter. So these values can be observed in the design footing in this way. So b1 is 4.89 meter b1 is 4.89 meter this is b2 that is 0.99 meter and the length of footing is 6.8 meter. Now here we will find this is a centroid of trapezoidal footing and just now we have seen that resultant of forces passing through center of this column and center of this column passes through centroid of this trapezoidal footing and hence it will give uniform pressure on this trapezoidal footing. Let us take some questions if the resultant of the soil pressure coincides with the resultant of the loads the soil pressure is assumed to be number 1 non-uniformly distributed, uniformly distributed 0 or none of the mentioned answer is uniformly distributed. Then two column loads are unequal, which of the following footing can be provided? Option 1 is trap footing, option 2 is rap footing, option 3 is trapezoidal combined footing and option 4 is mat footing and hence obvious trapezoidal combined footing. Third question for a trapezoidal combined footing x bar is given by l by 2 or in this case say l by 3 is less than x bar and that is less than l by 2, x bar is equal to l by 3 none of the mentioned answer l by 3 will be less than x bar and x bar will be again less than l by 2. These are the references which are used for drafting this presentation. Thank you.