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