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# DEFLECTION OF BEAM

now under the action of this load the beam is going to get we can say that the shape is going to change because of the action of load and I am considering the beam as elastic so when the load is acting the beam will deflect in this manner and when the load is removed the span will come back to its original position which is indicated here so here the first definition is deflection I will say that it is the vertical distance it is the vertical distance of the beam measured before and after loading.

so here we I have written the definition of deflection that it is the vertical distance of the beam measured before and after loading that is before loading the distances here and after loading it will reach at this location so this distance is called as deflection and it is denoted by Y in this chapter we are going to denote the deflection by Y so I can say that the deflection here is y next deflection at the supports is always zero at a and B the deflection would be zero so Y is equal to zero Y is equal to zero at a and B respectively next after the deflection definition.

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the next definition is of slope now slope is the angle turned by the beam this is Theta so here I will say that slope it is the angle in radians measured between the tangent here we have the tangent so the angle measured in radians between the tangent to the elastic curve to the elastic curve and the original axis of the beam so here as I can see that when the beam is bending under the action of load this curvature of the beam is called as elastic curve and tangent drawn to the elastic curve if we take the angle of this tangent with respect to the original axis of the beam that is called as the slope and here I can see that slope is denoted by angle theta or it is simply written as dy by DX next its unit is radiant now after reaching here next let us see the boundary conditions the next case is considering the boundary conditions for simply supported for simply supported beam and for cantilever beam now for the simply supported beam supported at a and B and suppose the load is acting at the center now under the action of this load the beam is having a length of capital L when the load is acting the beam is going to deflect and here I can say that the deflection at a and B is zero because it is simply supported so at a and B deflection is 0 that is here I have written the boundary condition for deflection next if I consider the center of this beam your deflection is maximum I’ll say this is Point C so at C deflection is maximum as we can see here and here when I am getting the deflection maximum if I draw the tangent the slope is zero so at C slope is zero then slope will be maximum at B and at a theta value so at a and B slope is maximum so here I have written the boundary conditions for a simply supported beam next for a cantilever span if the load is acting at the free end here we have point a this is point B considering the length of the beam as capital L now under the action of this load the beam will start to bend ahead of point a that is it will start bending from here and now I can say that first at a deflection is zero here and I can say that also at a even slope is zero slope is also 0 then at B Here I am getting the deflection as maximum at the free end for a cantilever beam the deflection is maximum so at B the deflection is max and at B the slope is also maximum because if I draw a tangent here to the elastic curve that will give me the maximum angle so at B the slope is also maximum so here in this video we have seen the various definitions for slope and deflection

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