Page 98 - Marks Calculation for Machine Design

P1: Sanjay
16:18
January 4, 2005
Brown.cls
Brown˙C02
80
two vertical reactions (A y and B y ). As the distributed load is acting directly downward, the
horizontal reaction (A x ) is zero. STRENGTH OF MACHINES
To provide a comparison between uniform loading on this beam and concentrated force
loading at the free end of the previous beam, the magnitude of the uniform load (w) has
been chosen to produce a total force equal to the concentrated force (F). Also, the beam
dimensions, material properties, and cross-sectional properties of this beam are the same
as the previous beam.
U.S. Customary SI/Metric
Example 1. Determine the reactions for a sin- Example 1. Determine the reactions for a sin-
gle overhanging beam of length (L) and over- gle overhanging beam of length (L) and over-
hang (a) with a uniformly distributed load (w), hang (a) with a uniformly distributed load (w),
where where
w = 113 lb/ft w = 1,540 N/m
L = 3 ft, a = 1ft L = 1m, a = 0.3 m
solution solution
Step 1. From Fig. 2.59 calculate the pin reac- Step 1. From Fig. 2.59 calculate the pin reac-
tions (A x and A y ) at the left end of the beam. tions (A x and A y ) at the left end of the beam.
As the uniform load (w) is vertical, As the uniform load (w) is vertical,
A x = 0 A x = 0
and the vertical reaction (A y ) is and the vertical reaction (A y ) is
2
2
2
2
w(L − a ) w(L − a )
A y = A y =
2L 2L
2
2
2
2
(113 lb/ft)[(3ft) − (1ft) ] (1,540 N/m)[(1m) − (0.3m) ]
= =
2 (3ft) 2 (1m)
2
2
2
2
(113 lb/ft)[9 ft − 1ft ] (1,540 N/m)[1 m − 0.09 m ]
= =
(6ft) (2m)
2
2
(113 lb/ft)[8 ft ] (1,540 N/m)[0.91 m ]
= =
(6ft) (2m)
904 ft · lb 1,402 N · m
= = 151 lb = = 701 N
6ft 2m
Step 2. From Fig. 2.59 calculate the roller Step 2. From Fig. 2.59 calculate the roller
reaction (B y ) as reaction (B y ) as
2
2
2
2
w (L + a ) w(L + a )
B y = B y =
2L 2L
(113 lb/ft)(3ft + 1ft) 2 (1,540 N/m)(1m + 0.3m) 2
= =
2 (3ft) 2 (1m)
(113 lb/ft)(4ft) 2 (1,540 N/m)(1.3m) 2
= =
(6ft) (2m)
2
2
(113 lb/ft)(16 ft ) (1,540 N/m)(1.69 m )
= =
(6ft) (2m)
1,808 ft · lb 2,602 N · m
= = 301 lb = = 1,301 N
6ft 2m