8-24. Determine the displacement at C and the slope at B. EI is constant. Use the

moment-area theorems.

Solution:

Using the M/EI diagram and elastic curve shown in Fig. a and b, respectively,

Theorem 1 and 2 give:

,

,

,

Then,

,

.

8-25. Solve Prob. 8–24 using the conjugate-beam method.

Solution:

The real beam and conjugate beam are shown in Fig.a and b, respectively. Referring to Fig.c,

,

,

Referring to Fig.d,

,

.

9–13. Determine the horizontal displacement of joint D. Assume the members are pin

connected at their end points. AE is constant. Use the method of virtual work.

Solution:

The virtual force and real force in each member are shown in Fig. a and b, respectively.

Member n (kN) N (kN) L (m) nNL ( )

AC 1.50 26.25 1.8 70.875

BC -1.25 -31.25 3 117.188

BD -0.75 -7.5 3.6 20.25

CD 1.25 12.5 3 46.875

255.188

,

,

.

9–14. Solve Prob. 9–13 using Castigliano’s theorem.

Solution:

Member N (kN) N (P=10 kN) L (m) N

L ( )

AC 1.5P+11.25 26.25 1.50 1.8 70.875

BC -(1.25P+18.75) -31.25 -1.25 3 117.188

BD -0.75P -7.5 -0.75 3.6 20.25

CD 1.25P 12.5 1.25 3 46.875

255.188

,

.

9–47. The L-shaped frame is made from two segments, each of length L and flexural

stiffness EI. If it is subjected to the uniform distributed load, determine the vertical

displacement of point B. Use the method of virtual work.

Solution:

The virtual force is shown in Fig. a and b and real force in each member is shown in Fig. c, d

and e, respectively.

,

,

.

9–48. Solve Prob. 9–47 using Castigliano’s theorem.

Solution:

P does not influence moment within vertical segment.

,

,

Set P=0,

.