Page 91 - Marks Calculation for Machine Design

P1: Sanjay
January 4, 2005
Brown˙C02
Brown.cls
2.2.7 Single Overhang: Concentrated Force
at Free End 16:18 BEAMS 73
The simply-supported beam in Fig. 2.51 has a single overhang on the right with a concen-
trated force (F) acting vertically downward at the free end, point C. The distance between
the supports is labeled (L), and the length of the overhang is labeled (a), so the total length
of the beam is (L + a).
F
A
C
B
L a
FIGURE 2.51 Single overhang: concentrated force at free end.

Reactions. The reactions at the supports are shown in Fig. 2.52—the balanced free-body-
diagram. Notice that the vertical reaction (A y ) is downward, whereas the vertical reaction
(B y ) is upward, and has a magnitude greater than the concentrated force (F). The force
(F) is acting straight down, so the horizontal reaction (A x ) is zero. If the force (F) had
a horizontal component, then the horizontal reaction (A x ) would be equal but opposite in
direction to this horizontal component.
F
A = 0
x

A = −Fa/L B = F(L + a)/L
y
y
FIGURE 2.52 Free-body-diagram.

U.S. Customary SI/Metric
Example 1. Determine the reactions for a sin- Example 1. Determine the reactions for a sin-
gle overhanging beam of length (L) and over- gle overhanging beam of length (L) and over-
hang (a) with a concentrated force (F) acting hang (a) with a concentrated force (F) acting
at the free end, where at the free end, where
F = 450 lb F = 2,000 N
L = 3 ft, a = 1ft L = 1m, a = 0.3 m
solution solution
Step 1. From Fig. 2.52 calculate the pin reac- Step 1. From Fig. 2.52 calculate the pin reac-
tions (A x and A y ) at the left end of the beam. tions (A x and A y ) at the left end of the beam.
As the force (F) is vertical, As the force (F) is vertical,
A x = 0 A x = 0
and the vertical reaction (A y ) is and the vertical reaction (A y ) is
Fa (450 lb)(1ft) Fa (2,000 N)(0.3m)
A y =− = A y =− =
L 3ft L 1m
450 ft · lb 600 N · m
=− =−150 lb =− =−600 N
3ft 1m