Page 119 - Marks Calculation for Machine Design

P1: Sanjay
January 4, 2005
Brown˙C02
Brown.cls
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0 16:18 BEAMS x 101
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–FL
FIGURE 2.88 Bending moment diagram.
U.S. Customary SI/Metric
Example 2. Calculate the shear force (V ) and Example 2. Calculate the shear force (V ) and
bending moment (M) for a cantilevered beam of bending moment (M) for a cantilevered beam of
length (L) with a concentrated force (F) acting length (L) with a concentrated force (F) acting
at its free end, at a distance (x) from the left end at its free end, at a distance (x) from the left end
of the beam, where of the beam, where
F = 150 lb F = 700 N
L = 8ft L = 2.5 m
x = 3ft x = 1m
solution solution
Step 1. Determine the shear force (V ) from Step 1. Determine the shear force (V ) from
Fig. 2.87 as Fig. 2.87 as
V =−F =−150 lb V =−F =−700 N
Step 2. Determine the bending moment (M) Step 2. Determine the bending moment (M)
from Eq. (2.59). from Eq. (2.59).
M =−Fx =−(150 lb)(3ft) M =−Fx =−(700 N)(1m)
=−450 ft · lb =−700 N · m

Example 3. Calculate and locate the max- Example 3. Calculate and locate the max-
imum shear force (V max ) and the maximum imum shear force (V max ) and the maximum
bending moment (M max ) for the beam of bending moment (M max ) for the beam of
Examples 1 and 2, where Examples 1 and 2, where
F = 150 lb F = 700 N
L = 8ft L = 2.5 m
solution solution
Step 1. Calculate the maximum shear force Step 1. Calculate the maximum shear force
(V max ) from Eq. (2.58) as (V max ) from Eq. (2.58) as
V max = F = 150 lb V max = F = 700 N

Step 2. Figure 2.87 shows that this maximum Step 2. As shown in Fig. 2.87, this maximum
shear force (V max ) of 150 lb does not have a shear force (V max ) of 700 N does not have a
specific location. specific location.
Step 3. Calculate the maximum bending Step 3. Calculate the maximum bending
moment (M max ) from Eq. (2.60) as moment (M max ) from Eq. (2.60) as
M max = FL = (150 lb)(8ft) M max = FL = (700 N)(2.5m)
= 1,200 ft · lb = 1,750 N · m