Page 77 - Marks Calculation for Machine Design

P1: Sanjay
January 4, 2005
Brown˙C02
Brown.cls
A 16:18 BEAMS w 59
B
D
L
FIGURE 2.36 Beam deflection diagram.
where = deflection of beam (positive downward)
w = applied uniform load
x = distance from left end of beam
L = length of beam
E = modulus of elasticity of beam material
I = area moment of inertia of cross-sectional area about axis through centroid

The maximum deflection ( max ) caused by this loading configuration is given by
Eq. (2.23),

5 wL 4 L
max = at x = (2.23)
384 EI 2
located at the midpoint (L/2).

U.S. Customary SI/Metric
Example 4. Calculate the deflection ( ) at Example 4. Calculate the deflection ( ) at
a distance (x) equal to (2L/3) for a simply- a distance (x) equal to (3L/5) for a simply-
supported beam of length (L) with a uniform supported beam of length (L) with a uniform
load (w) across the entire beam, where load (w) across the entire beam, where
w = 400 lb/ft w = 6,000 N/m
L = 15 ft L = 5m
2
6
9
2
E = 10.3 × 10 lb/in (aluminum) E = 71 × 10 N/m (aluminum)
I = 12 in 4 I = 469 cm 4
solution solution
Step 1. Determine the distance (x). Step 1. Determine the distance (x).
2L 2 (15 ft) 30 ft 3L 3(5m) 15 m
x = = = = 10 ft x = = = = 3m
3 3 3 5 5 5
Step 2. Calculate the stiffness (EI). Step 2. Calculate the stiffness (EI).
2
9
4
6
4
2
EI = (10.3 × 10 lb/in )(12 in ) EI = (71 × 10 N/m )(469 cm )
1ft 2 1m 4
8 2
= 1.24 × 10 lb · in × 2 × 4
144 in (100 cm)
5
5
= 8.58 × 10 lb · ft 2 = 3.33 × 10 N · m 2