Page 68 - Marks Calculation for Machine Design

P1: Sanjay
16:18
January 4, 2005
Brown.cls
Brown˙C02
STRENGTH OF MACHINES
50
a
b
B = 0
C x
A = C/L B = –C/L
y
y
FIGURE 2.26 Free-body-diagram.
V
C/L
+ L
0 x

FIGURE 2.27 Shear force diagram.
Note that the shear force (V ) is a constant (C/L) from the left end of the beam to the right
end of the beam. As the couple is not a force, its location does not affect the shear force distri-
bution, unlike a concentrated force that causes a discontinuity in the shear force distribution
where the force acts. Therefore, the maximum shear force (V max ) is given by Eq. (2.12).
C
V max = (2.12)
L
The bending moment (M) distribution is given by Eq. (2.13a) for the values of the distance
(x) from the left end of the beam to where the couple acts and Eq. (2.13b) from where the
couple acts to the right end of the beam. (Always measure the distance (x) from the left
end of any beam.)
C
M = x 0 ≤ x ≤ a (2.13a)
L
C
M =− (L − x) a ≤ x ≤ L (2.13b)
L
The bending moment (M) distribution is shown in Fig. 2.28.

M
Ca/L

+ b
0 x
a L
−

−Cb/L

FIGURE 2.28 Bending moment diagram.