Page 128 - Marks Calculation for Machine Design

P1: Sanjay
January 4, 2005
16:18
Brown.cls
Brown˙C02
STRENGTH OF MACHINES
110
2.3.3 Concentrated Couple
The cantilevered beam shown in Fig. 2.97 has an applied couple (C) acting clockwise (cw)
at a distance (a) from the cantilevered support at point A. The distance from the couple
to the free end of the beam at point B is labeled (b), and the total length of the beam is
labeled (L).
C
A B
a b
L
FIGURE 2.97 Concentrated couple.
Reactions. The reactions at the support are shown in Fig. 2.98—the balanced free-body-
diagram. As the only load on the beam is a couple, the horizontal and vertical reactions
(A x and A y ) are equal to zero, and the couple reaction (C A ) is equal to magnitude of the
applied couple (C), but opposite to its direction, meaning counterclockwise (ccw). (Recall
that counterclockwise is considered positive.)
The location of the applied couple (C) along the beam does not affect the reactions or
the shear force distribution, but only affects the bending moment distribution and the shape
of the deflection curve.

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 an applied tilevered beam of length (L) with an applied
couple (C) acting at a distance (a) from the couple (C) acting at a distance (a) from the
support, where support, where
C = 1,500 ft · lb C = 2,000 N · m
L = 4ft L = 1.2 m
a = 3 ft, b = 1ft a = 0.9 m, b = 0.3 m
solution solution
From Fig. 2.98 calculate the reactions (A x , A y , From Fig. 2.98 calculate the reactions (A x , A y ,
and C A ) at the left end of the beam. and C A ) at the left end of the beam.
Step 1. As the couple (C) is the only load Step 1. As the couple (C) is the only load
acting on the beam, acting on the beam,
A x = 0 A x = 0
and and
A y = 0 A y = 0
Step 2. Therefore the couple (C A ) is Step 2. Therefore, the couple (C A ) is
C A = C = 1,500 ft · lb C A = C = 2,000 N · m
Note that as (C A ) is positive, this means it is Note that as (C A ) is positive, this means it is
counterclockwise (ccw). counterclockwise (ccw).