Page 117 - Marks Calculation for Machine Design

P1: Sanjay
January 4, 2005
Brown˙C02
Brown.cls
A F 16:18 BEAMS B 99
L
FIGURE 2.83 Concentrated force at free end.

Reactions. The reactions at the support are shown in Fig. 2.84—the balanced free-body-
diagram. Notice that the vertical reaction (B y ) is equal to the force (F), and because the
force (F) is acting straight down, the horizontal reaction (B x ) is zero. If the force (F) had a
horizontal component, either left or right, then the horizontal reaction (B x ) would be equal,
but opposite in direction, to this horizontal component. The couple reaction (C B ) is in a
negative direction, meaning clockwise (cw), and equal to a negative of the force (F) times
the length of the beam (L).

F
B = 0
x
C = –FL
B
B y = F
FIGURE 2.84 Free-body-diagram.

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 concentrated tilevered beam of length (L) with a concentrated
force (F) acting at its free end, where force (F) acting at its free end, where
F = 150 lb F = 700 N
L = 8ft L = 2.5 m
solution solution
From Fig. 2.84 calculate the reactions (B x , B y , From Fig. 2.84 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 force (F) is vertical, Step 1. As the force (F) is vertical,
B x = 0 B x = 0
and and
B y = F = 150 lb B y = F = 700 N

Step 2. The couple (C B ) is given by Step 2. The couple (C B ) is given by
C B =−FL =−(150 lb)(8ft) C B =−FL =−(700 N)(2.5m)
=−1,200 ft · lb =−1,750 N · m
Notethattheminussignmeansitisclockwise Notethattheminussignmeansitisclockwise
(cw). (cw).