Structural Analysis Methods II: Structural Systems - Mechanics of Structures: Variational and Computational Methods - page 324

FIGURE P5.24
Plane truss

FIGURE P5.25
A pin-jointed truss.

Answer:
Displacements:
U Xb =−

10 − 3 10 − 4

1 . 273 × in. U Xc = 7 . 273 × in.

10 − 3 10 − 3 U Zb =− 6 . 636 × in. U Zc =− 3 . 636 × in.

Bar Forces: Bar Stresses:

N 1

1

36 lb/in. 2

=− 636 . 36 lb (compression) σ =− 636 .

73 lb/in. 2 N 2

2

=+ 899 . 95 lb (tension) σ =+ 1272 .

64 lb/in. 2 N 3

3

=+ 363 . 64 lb σ =+ 363 .

27 lb/in. 2 N 4

4

=− 514 . 26 lb σ =− 727 .

64 lb/in. 2

N 5

5

=+ 363 . 64 lb σ =+ 363 .

N 6

6

= 0 σ = 0

Beams

5.26 Compute the deflection of the free end of the stepped beam of Chapter 3, Fig. 3.10c.
Express your answer in terms of general symbols such as EI beam 1 .
5.27 Calculate the reactions of the beam of Chapter 3, Fig. P3.27.
5.28 Find the reactions at the ends and at the hinge of the beam of Chapter 3, Fig. P3.1.
5.29 Compute the displacement and reaction at the left end of the beam of Chapter 3,
Fig. P3.26. If the spring is

s units too long before the load is applied, what will be the
magnitude of the reactions?
5.30 Suppose a be am element undergoes a change in temperature

v

T . Show that the load-
ing vector p i 0 corresponding to a stiffness matrix for a beam element of bisymmetric