472
SOLUTION
The primary real beam and qualitative influence line are
shown in Fig. a and its conjugate beam is shown in Fig. b.
Referring to Fig. c,
1
3
*9–44. Draw the influence line for the moment at A. Plot
numerical values at the peaks. Assume A is fixed and the
support at B is a roller. EI is constant.
A B
3 m 3 m
473
SOLUTION
9–45. Draw the influence line for the vertical reaction at B.
Plot numerical values at the peaks. Assume A is fixed and the
support at B is a roller. EI is constant.
A B
3 m 3 m
475
SOLUTION
The primary real beam and qualitative influence line are
shown in Fig. a, and its conjugate beam is shown in Fig. b.
Referring to Figs. c, d, e, and f,
6.1875
22.5
9–47 Draw the influence line for the shear at C. Plot
numerical values every 1.5 m. Assume A is fixed and the
support at B is a roller. EI is constant.
BAC
3 3m m
476
SOLUTION
*9–48. Sketch the influence line for (a) the vertical reaction
at C, (b) the moment at B, and (c) the shear at E. In each case,
indicate on a sketch of the beam where a uniform distributed
live load should be placed so as to cause a maximum positive
value of these functions. Assume the beam is fixed at F. EI is
constant.
2 m
AB
CD
EF
2 m4 m 2 m 2 m
477
SOLUTION
9–49. Sketch the influence line for (a) the vertical reaction at
C, (b) the moment at B, and (c) the shear at E. In each case,
indicate on a sketch of the beam where a uniform distributed
live load should be placed so as to cause a maximum positive
value of these functions. Assume the beam is fixed at F. EI is
constant.
2 m
A
BCD
EF
2 m4 m 2 m 2 m
478
SOLUTION
9–50. Use the Müller-Breslau principle to sketch the general
shape of the influence line for the moment at A.A
479
SOLUTION
9–51. Use the Müller-Breslau principle to sketch the general
shape of the influence line for the moment at A and the shear
at B.
A
B
480
SOLUTION
*9–52. Use the Müller-Breslau principle to sketch the general
shape of the influence line for the shear at A and the moment
at B.
A
B
481
SOLUTION
9–53. Use the Müller-Breslau principle to sketch the general
shape of the influence line for the moment at A and the shear
at B.
B
A