Advanced Methods of Structural Analysis

268 7 The Force Method

7.25.A rigid horizontal beam is supported by four identical vertical rods and sup-
ports a loadP, as shown in Fig.P7.25. The stiffnessEAis constant for all vertical
rods. Determine the axial forces in members 1-4. Neglect the weight of the beam.

P

d d d l

1 2 3 4

Fig. P7.25

Ans.N 1 D0:4PI N 2 D0:3PI N 3 D0:2PI N 4 D0:1P

7.26.A beam with clamped supportAand elastic supportBis subjected to unit
angular displacement of clamped support (Fig.P7.26). The flexural stiffnessEIis
constant; stiffness of elastic support isk.RBDkB/; and the length of the beam
isl:Construct the bending moment diagram. Consider limiting cases (kD 0 ,and
kD/).

j =1

EI, l

k

A B

Fig. P7.26

Ans.MAD

3 EI

l



1

1 C ̨

; ̨D

3 EI

kl^3

.

7.27.The tieabof a truss is subjected to thermal gradientt, degrees. Axial stiff-
ness of the upper and lower chords of the truss is 2EA; for all other members of the
structure axial stiffness isEA.Calculate the axial force at the memberab.

EA

d

h

=3m

2 EA

2 EA

EA

EA

Δt

2m

a b

d=4m

Fig. P7.27

Ans.X 1 D0:152 ̨tEA