 So today I am going to discuss on analysis and design of two slab for a cantilever retaining wall. At the end of this session learners will be able to analyze and design the two slab of cantilever retaining wall. Introduction. The soil reaction varies linearly. So this is the soil reaction which varies linearly with more pressure on toe end. That means this is toe slab, this is stem slab, this is heel slab of a cantilever retaining wall. So at the end of toe slab you find maximum pressure and at the end of heel slab you find minimum pressure. So this is due to earth pressure on stem slab, so which is this is figure one. In figure one we have shown the stress, the earth pressure it is there in this. So this is earth pressure, pH is earth pressure. So due to earth pressure you find the p by a that is m by z that is the maximum pressure p1 you will get and the minimum pressure you will get on this particular side. The basic design principle of cantilever retaining wall is to see that the pressure at the end of the heel slab is never negative. That means it should not lose the contact since soil cannot apply negative earth pressure. So therefore the retaining wall should not leave the soil that means it should remain with the founding soil. So that means this reaction p2 can be 0, it cannot be negative. If it is negative then it will get lifted up, so that is not at all possible. So if the earth pressure is negative, the stability of the structure itself is in doubt. So structure will not be stable if earth pressure is negative. So therefore you should see that the minimum pressure that is p2 should be either 0 or it should be greater than 0. That is what we should observe. So apart from soil pressure direct weights of backfill and the surcharge of the wheel are also considered in the design. So this is shown in figure number two. Figure number two shows so this is w1 weight of soil, w2, w3 weight of stem, w4 weight of base slab and this is pH is earth pressure. So we are supposed to carry out first we should assume the dimensions of the retaining wall by thumb rule and then afterwards we have to do stability analysis. So when we find the structure is stable further we go for design of stem slab, design of toes slab and design of heel slab. So I have already created a video for stability analysis. You please go through the stability analysis so that you will understand how to find the reactions and everything. So next analysis of toes slab. So where is the maximum moment in the toes slab? If you just observe the figure one so this is toes slab from here to here of length l1. So up to the face of the stem slab this is a toes slab. So where will be the maximum bending moment for this particular toes slab when it is subjected to pressure p1 here and pressure p3 here. So where will be the maximum bending moment? Just think of the maximum bending moment in the toes slab will be at the face of the stem slab. At the face of the stem slab you find the maximum bending moment it is a cantilever of length l1 which is a hogging bending moment. So because it will try to lift up the toe portion. The pressure is upward therefore it will try to lift up. So taking moment about the face of the stem slab m is equal to p1 into l1 square by 2 is p1 isn't it? So therefore here it will be p3 into l1 square by 2 that will be the pressure due to UDL then p4 into 2 third l1. So this is the p4 node p4 node this is at 2 third l1 of a triangular portion. So we will find out the maximum bending moment. So mu is equal to 1.5 times m where what is E? E is nothing but eccentricity eccentricity is B by 2 that is base width divided by 2 minus sigma ms minus sigma mo divided by mw. So ms is the stabilizing moment some of stabilizing moment mo is stem slab over turning moment. And the algebraic sum of these two divided by the weight downward weight that will give us eccentricity E is equal to B by 2 minus this. Then p1 is equal to sigma w total weight downward divided by B into 1 plus 6E by B. So this should be less than SBC of soil and p2 is sigma w by B into 1 minus 6E by B this should be greater than or equal to 0. And p3 is the force which is at the face of the stem pressure at the face of the stem. So it is p2 plus p1 minus p2 divided by B into B minus l1 and p4 is the area of the triangular diagram it is half l1 into p1 minus p3. Now the design of tow slab equating MU limit with MU. MU limit it depends upon the formula it is 0.418 fckbd square if it is mild steel 0.138 fckbd square if it is hysd415 and it is 0.133 fckbd square if it is hysd bars 500 fe 500. Find the effective depth required and compare it we have to by equating MU limit with MU. So we find the effective depth required and we will compare it with the whatever we have provided in preliminary dimensions for which we have done already the stability analysis. Which shall be greater the provided dimension should be greater than or equal to the effective depth required. Now determine area of steel by using g.1.1b. So if we find that if it is MU is less than MU limit so we will find that you will be having the under reinforced section then we will find out the area of steel is determined by this equation. And it is also to be compared with EST minimum because distribution steel is EST minimum 0.12 by 100 into B into D and B is always taken 1 meter that is 1000 mm. Provide design steel at bottom and minimum steel as a distribution steel perpendicular to it as shown in figure number 3. So this is figure number 3. So figure number 3 this is your tow slab and here design steel will be at the bottom and the distribution steel will be perpendicular to it. So both are same that means in this particular case the design steel is less than usually the span is less L1 is less therefore design steel is less than the minimum steel therefore we have provided same steel as the steel on let the side as well as perpendicular to it. So these are the references used for preparation of this particular video. And thank you very much.