Page 129 - Marks Calculation for Machine Design

P1: Sanjay
January 4, 2005
16:18
Brown.cls
Brown˙C02
A
A = 0 C = C BEAMS C 111
x
A = 0
y
FIGURE 2.98 Free-body-diagram.
Shear Force and Bending Moment Distributions. For the cantilevered beam, with an
applied couple (C) acting clockwise (cw) at a distance (a) from the support, shown in
Fig. 2.99, which has the balanced free-body-diagram shown in Fig. 2.100, the shear force
(V ) distribution is shown in Fig. 2.101.
C
A B

a b
L
FIGURE 2.99 Concentrated force at intermediate point.

C = C
A = 0 A C
x

A = 0
y
FIGURE 2.100 Free-body-diagram.

Note that the shear force (V ) is zero from the left end of the beam to the right end of the
beam. This is because the reactions (A x and A y ) are zero, which is because the only load
on the beam is an applied couple.
The bending moment (M) starts at the left end of the beam with a negative value of the
couple (−C) and continues at this value for a distance (a). At this point where the applied
couple acts, the bending moment becomes zero, and continues at this value to the right end
of the beam.
The bending moment (M) distribution is shown in Fig. 2.102.
The maximum bending moment (M max ) occurs in the region to the left of the applied
couple (C) and given by Eq. (2.69).
M max = C (2.69)

V

0 x
L

FIGURE 2.101 Shear force diagram.