Page 138 - Marks Calculation for Machine Design

P1: Sanjay
January 4, 2005
Brown˙C02
Brown.cls
120
U.S. Customary 16:18 STRENGTH OF MACHINES SI/Metric
Step 2. Determine the deflection ( ) from Step 2. Determine the deflection ( ) from
Eq. (2.77). Eq. (2.77).
w 4 3 4 w 4 3 4
= (x − 4 L x + 3L ) = (x − 4 L x + 3L )
24 (EI) 24 (EI)
(50 lb/ft) (800 N/m) 4
= = [(1.2m)
2
2
6
6
24 (2.5 × 10 lb · ft ) 24 (1.5 × 10 N · m )
4
4
3
4
3
×[(4ft) − 4 (5ft) (4ft) + 3 (5ft) ] − 4(1.5m) (1.2m) + 3(1.5m) ]
(50 lb/ft) (800 N/m)
= =
2
7
2
7
(6 × 10 lb · ft ) (3.6 × 10 N · m )
4
4
× [(256 − 2,000 + 1,875) ft ] ×[(2.0736 − 16.2 + 15.1875) m ]

1 −5 1 4

4
= 8.33 × 10 −7 × (131 ft ) = 2.22 × 10 3 × (1.0611 m )
ft 3 m
12 in 100 cm
= 0.00011 ft × = 0.0000235 m ×
ft m
= 0.0013 in ↓ = 0.0024 cm ↓
Example 5. Calculate the maximum deflec- Example 5. Calculate the maximum deflec-
tion ( max ) and its location for the beam tion ( max ) and its location for the beam
configuration in Example 4, where configuration in Example 4, where
w = 50 lb/ft w = 800 N/m
L = 5ft L = 1.5 m
6
6
EI = 2.5 × 10 lb · ft 2 EI = 1.5 × 10 N · m 2
solution solution
Step 1. Calculate the maximum deflection at Step 1. Calculate the maximum deflection at
the free end from Eq. (2.78). the free end from Eq. (2.78).
wL 4 wL 4
max = max =
8 (EI) 8 (EI)
(50 lb/ft)(5ft) 4 (800 N/m)(1.5m) 4
= =
2
2
5
6
8 (2.5 × 10 lb · ft ) 8 (1.5 × 10 N · m )
31,250 lb · ft 3 4,050 N · m 3
= = 7 2
7
2 × 10 lb · ft 2 1.2 × 10 N · m
12 in 100 cm
= 0.0016 ft × = 0.00034 m ×
ft m
= 0.019 in ↓ = 0.034 cm ↓
2.3.5 Triangular Load
The cantilevered beam shown in Fig. 2.111 has a triangular distributed load (w) acting
vertically downward across the entire length (L). The unit of this distributed load (w) is
force per length. As the distribution is triangular, the total force acting on the beam is one
1
half ( / 2) times the uniform load (w) times the length of the beam (L),or(wL/2). For finding
1
the reactions, this total load is considered to be located at a point one-third ( / 3) the distance
from the right end of the beam, or (L/3).