Question 20.P.13: Fig. P.20.13(a) represents a bridge structure with a suspend...
Fig. P.20.13(a) represents a bridge structure with a suspended span so that C and D are hinged connections. Sketch dimensioned influence lines for the vertical reactions at A and B and the shearing force at the hinge C.
The truss shown in Fig. P.20.13(b) is supported at A, E and H. A scale model of the truss, supported at A and H only, was loaded by a vertical load at E which produced the following values of deflection:
\begin{array}{llllllll} A & B & C & D & E & F & G &H\end{array} \\ \begin{array}{llllllll}0 & 10 & 16 & 21 & 27 & 20 & 13 & 0\end{array}Plot the unit influence line for the vertical reaction at E in the real truss and hence find its value when concentrated loads of 120 kN at B and 160 kN at C are applied. For this loading system find the values of the axial force in the members JC and JK.
The required unit influence lines are shown in Fig. S.20.13(a).
The influence line for the vertical reaction at E in the truss is shown in Fig. S.20.13(b).
With the 120 kN load at B and the 160 kN load at C
R_{\mathrm{E}}=120 \times \frac{10}{27}+160 \times \frac{16}{27}=139.3 \mathrm{\ kN}
Then, taking moments about H
7 \times 3 R_{\mathrm{A}}+3 \times 3 \times 139.3=6 \times 3 \times 120+5 \times 3 \times 160
which gives
R_{\mathrm{A}}=157.4 \mathrm{\ kN}
At a vertical section through the member JC the shear force is equal to R_{A} – 120.
Therefore
F_{\mathrm{JC}} \sin 60^{\circ}=157.4-120 (see Section 4.7; Method of Sections)
from which
F_{\mathrm{JC}}=43.2 \mathrm{\ kN} \text { (tension) }
Now taking moments about C and considering a vertical section through CK
F_{\mathrm{JK}} \times 1.5 \tan 60^{\circ}=157.4 \times 6-120 \times 3
so that
F_{\mathrm{JK}}=224.9 \mathrm{kN} \text { (compression) }
