A continuous beam ABC is carrying a uniformly distributed load of 1 kN/m in addition to a concentrated load of 10kN as shown in Fig.7.5a, Draw bending moment and shear force diagram. Assume EI to be constant for all members.

 A continuous beam ABC is carrying a uniformly distributed load of 1 kN/m in addition to a concentrated load of 10kN as shown in Fig.7.5a, Draw bending moment and shear force diagram. Assume EI to be constant for all members.

It is observed that the continuous beam is statically indeterminate to first degree. Choose the reaction at B, RBy as the redundant. The primary structure is a simply supported beam as shown in Fig.1.11. Now, compute the deflection at B, in the released structure due to uniformly distributed load and concentrated load. This is accomplished by unit load method. Thus,

In thenextstep, apply a unit load at B in the direction of

RBy(upwards)and

 

Calculate the deflection at B of the following structure. Thus(seeFig.7.5c),

Now, deflection at B in the primary structure due to redundant       RB  is,

In the actual structure, the deflection at B is zero. Hence, the compatibility equation may be written as

L+  B=0(4)

 

The other two reactions are calculated by static equilibrium equations (videFig.

 

1.13)

RA =7.8125kN

RB =2.8125kN