Page 66 - Marks Calculation for Machine Design

P1: Sanjay
January 4, 2005
Brown˙C02
Brown.cls
48
U.S. Customary 16:18 STRENGTH OF MACHINES SI/Metric
Example 6. Calculate the deflection ( a ) at Example 6. Calculate the deflection ( a ) at
the location (a) where the force (F) acts, where the location (a) where the force (F) acts, where
F = 10 kip = 10,000 lb F = 45 kN = 45,000 N
L = 8 ft, a = 6 ft, b = 2ft L = 3m, a = 2m, b = 1m
5
5
EI = 8.33 × 10 lb · ft 2 EI = 4.16 × 10 N · m 2
solution solution
Calculate the deflection ( a ) where the force Calculate the deflection ( a ) where the force
(F) acts from Eq. (2.11). (F) acts from Eq. (2.11).
2 2
2 2
Fa b Fa b
a = a =
3 (EI) L 3 (EI) L
2
2
(10,000 lb)(6ft) (2ft) 2 (45,000 N)(2m) (1m) 2
= =
2
2
5
5
3 (8.33 × 10 lb · ft )(8ft) 3 (4.16 × 10 N · m )(3m)
6
1.44 × 10 lb · ft 4 180,000 N · m 4
= =
7
6
2.00 × 10 lb · ft 3 3.74 × 10 N · m 3
12 in 100 cm
= 0.072 ft × = 0.86 in ↓ = 0.0481 m × = 4.81 cm ↓
ft m
Notice that the maximum deflection ( max ) found in Example 5 is greater than the
deflection ( a ) found in Example 6, which shows conclusively that the maximum deflection
does not occur where the force (F) acts.
2.2.3 Concentrated Couple
The simply-supported beam in Fig. 2.23 has a concentrated couple (C) acting counter-
clockwise at an intermediate point, not at its midpoint. The distance between the supports
is labeled (L), so the couple (C) is located at a distance (a) from the left end of the beam
and a distance (b) from the right end of the beam, where the sum of distances (a) and (b)
is equal to the length of the beam (L).
a b
C
A B
L
FIGURE 2.23 Concentrated couple at intermediate point.

Reactions. The reactions at the end supports are shown in Fig. 2.24—the balanced free-
body-diagram. Notice that as the couple (C) is counterclockwise, the pin support must be
located at the right end of the beam, with the roller support at the left. Notice that the vertical
reactions (A y and B y ) are equal in magnitude but opposite in direction, and as there is no
force acting on the beam, the horizontal reaction (B x ) is zero.