Advanced Methods of Structural Analysis

266 7 The Force Method

Ans.QAD32:99kN;QBD3:02kN;QCD5:32kN;

NCDD50:03kN.

7.20.Symmetrical structure is subjected to loadP, as shown in Fig.P7.20.The
cross-sectional area of the vertical member isA, and for inclined members arekA,
wherekis any positive number. The length of inclined members isl. Calculate the
internal force in the vertical member.

aa

A

kA kA, l

P

Fig. P7.20

Ans.NvertD

P

1 C2kcos^3 ̨

.

7.21.The structure consists of the truss, which is supported at points 1 and 7, and
the above truss construction. The structure carries five concentrated loadsP,which
are applied at joints 2-6 of the upper chord of the truss. Axial stiffness for upper
and lower chords of the truss is 2EA, for vertical and diagonal elements of the truss
and the above truss construction isEA.Provide a kinematical analysis. Determine
internal force in the member 4-c.

(^1234)
4
4m
7
4
6
4
5
4
PP P P P
1m
2m
3m
3m
2 ′ 3 ′ 4 ′ 5 ′ 6 ′
a
b
c
d
e
Fig. P7.21
Ans.X 1 D0:916P.
7.22.Uniform semicircular arch with fixed ends is loaded by uniform loadq
(Fig.P7.22). Calculate reactions of supports. Construct the internal force diagrams