Page 134 - Marks Calculation for Machine Design

P1: Sanjay
January 4, 2005
16:18
Brown.cls
Brown˙C02
STRENGTH OF MACHINES
116
the uniform load (w) is acting straight down, the horizontal reaction (B x ) is zero. The couple
reaction (C B ) is in a negative direction, meaning clockwise (cw), and equal to a negative
2
of the uniform load (wL) times the distance (L/2), or (−wL /2).
U.S. Customary SI/Metric
Example 1. Determine the reactions for a can- Example 1. Determine the reactions for a can-
tilevered beam of length (L) with a uniform tilevered beam of length (L) with a uniform
distributed load (w), where distributed load (w), where
w = 50 lb/ft w = 800 N/m
L = 5ft L = 1.5 m
solution solution
From Fig. 2.105 calculate the reactions (B x , B y , From Fig. 2.105 calculate the reactions (B x , B y ,
and C B ) at the right end of the beam. and C B ) at the right end of the beam.
Step 1. As the uniform load (w) is acting Step 1. As the uniform load (w) is acting
vertically downward, vertically downward,
B x = 0 B x = 0
and and
B y = wL = (50 lb/ft)(5ft) B y = wL = (800 N/m)(1.5m)
= 250 lb = 1,200 N
Step 2. The couple (C B ) is given by Step 2. The couple (C B ) is given by
wL 2 (50 lb/ft)(5ft) 2 wL 2 (800 N/m)(1.5m) 2
C B =− =− C B =− =−
2 2 2 2
1,250 ft · lb 1,800 N · m
=− =−625 ft · lb =− =−900 N · m
2 2
Note that the minus sign on (C B ) means it is Notethattheminussignmeansitisclockwise
clockwise (cw). (cw).

w
A B

L
FIGURE 2.106 Uniform load.
Shear Force and Bending Moment Distributions. For the cantilevered beam with a
uniform distributed load (w) acting across the entire length of the beam (L), shown in
Fig. 2.106, which has the balanced free-body-diagram shown in Fig. 2.107, the shear force
(V ) distribution is shown in Fig. 2.108.
w
B = 0
x
2
C = –wL /2
B
B = wL
y
FIGURE 2.107 Free-body-diagram.