Solutions For Fundamentals of Structural Analysis Chapter 10 Problem 13P

As there is no load acting in the frame, there will be no P system for the frame, thus to compute the horizontal displacement at the joint B, assume a dummy unit load to be acting at the joint B of the frame.

Draw the reaction diagram of Q system for horizontal deflection at B:

Consider the horizontal force equilibrium:

…… (1)

Consider the moment about the support A:

Substitute 0.67 kips for in equation (1).

Equate the deflection in the structure by using the relation:

…… (2)

Here, the sum of all the dummy moments , the moment about the beam taken from the Q system is , the moment about the beam taken from the P system is , the modulus of elasticity is E, and the moment of inertia of the beamis I.

As there are no specific conditions applied to the structure for the deflection, the moment due to P-system and Q system will be equal to zero.

Rearrange the equation:

Calculate the horizontal component of displacement using the formula:

Substitute for and for .

Therefore, the horizontal deflection of the joint at B is.

As there is no load acting in the frame, there will be no P system for the frame, thus to compute the vertical displacement at the joint B, assume a dummy unit load Q = 1 kip to be acting at the joint B of the frame.

Draw the reaction diagram of Q system for vertical deflection at B:

Consider the vertical force equilibrium:

Consider the horizontal force equilibrium:

…… (3)

Consider the moment about the support A:

Substitute 0.5 kips for R_DH in equation (3):

As there are no specific conditions applied to the structure for the deflection, the moment due to P-system and Q system will be equal to zero.

Calculate the horizontal component of displacement using the formula:

Substitute for and for .

Therefore, the vertical deflection of the joint at B is.

As there is no load acting in the frame, there will be no P system for the frame, thus to compute the change in slope of member BC, assume a dummy unit moment Q = 1 kip-ft to be acting at the joint B of the frame.

Draw the reaction diagram of Q system for change in slope of member BC:

As the moment acting at the point B is in clockwise direction, the reaction at A and D will be in anti-clockwise direction.

The reaction at the support A and D is equal to the ratio of moment acting in the beam to the total span.

The reaction at the support A, is and the reaction at the support D, is .

Substitute 1 kip-ft for M and 30 ft for Lin :

The reaction at the support A is , similarly the reaction at the support D is .

As there are no specific conditions applied to the structure for the deflection, the moment due to P-system and Q system will be equal to zero.

Rearrange the equation:

Substitute for and for .

Therefore, the slope in the member BC is.