Page 118 - Marks Calculation for Machine Design

P1: Sanjay
January 4, 2005
Brown˙C02
Brown.cls
100
A F 16:18 STRENGTH OF MACHINES B
L
FIGURE 2.85 Concentrated force at free end.

Shear Force and Bending Moment Distributions. For the cantilevered beam with a
concentrated force (F) at its free end, shown in Fig. 2.85, which has the balanced free-
body-diagram shown in Fig. 2.86, the shear force (V ) distribution is shown in Fig. 2.87.

F
B = 0
x

C = –FL
B
B = F
y
FIGURE 2.86 Free-body-diagram.
V

0 x
L
–
–F

FIGURE 2.87 Shear force diagram.
Note that the shear force (V ) is a negative (F) from the left end of the beam across to
the right end of the beam. The maximum shear force (V max ) is therefore
V max = F (2.58)

The bending moment distribution is given by Eq. (2.59) for the values of the distance (x)
equal to zero at the left end of the beam to a value (L) at the right end of the beam. (Always
measure the distance (x) from the left end of any beam.)
M =−Fx 0 ≤ x ≤ L (2.59)

The bending moment (M) distribution is shown in Fig. 2.88.
Note that the bending moment (M) is zero at the left end of the beam, where the force
(F) acts, then decreases linearly to a maximum negative value (−FL) at the right end. The
maximum bending moment (M max ) occurs at the right end of the beam and is given by
Eq. (2.60).
M max = FL (2.60)