Geoscience Reference
In-Depth Information
■
EXAMPLE 11.14
Problem:
A rectangular beam that is 12 ft long by 6 in. high by 3 in. wide has a 2-ton concentrated
load applied at its center. What is the maximum bending stress on this beam?
Solution:
M
=
PL
/4 = [(4000 lb)(12 ft. × 12 in./ft)]/4 = 144,000 in.-lb
C/L
= 6/
bD
2
(from applicable table) = 6/[(3 in.)(6 in.)
2
] = 0.05555 in.
3
σ =
MC
/
L
= (144,000 in.-lb)(0.05555 in.
3
) = 7999 psi.
11.6.11 r
eaCtion
F
orCe
(b
eams
)
11.6.11.1 Uniform Loading
Unknown forces exerted upward by the supports at each end of a beam to hold it up are called
reactions
. Known forces that act on beams are called
loads
. Reactions balance the load to keep the
beam in a state of equilibrium. To determine the reactions on a beam's supports we use the follow-
ing equation:
R
L
=
R
R
=
WL
/2
(11.15)
where
R
L
= Left reaction (lb).
R
R
= Right reaction (lb).
W
= Uniform weight loading per foot of the bean (lb/ft).
L
= Length of the beam (ft).
■
EXAMPLE 11.15
Problem:
A 10-ft-long beam supported at two points, one at each end, is uniformly loaded at a rate
of 200 lb/ft. What are the reactions on the supports?
Solution:
R
L
=
R
R
=
WL
/2 = [(200 lb/ft)(10 ft)]/2 = 1000 lb
11.6.11.2 Concentrated Load at Center
To calculate the reactions
R
L
and
R
R
in simple beams (those beams supported by two points, one at
each end) of any length that are loaded at their center with a concentrated load, we use the following
equation.
R
L
=
R
R
=
P
/2
(11.16)
where
R
L
= Left reaction (lb).
R
R
= Right reaction (lb).
P
= Concentrated load at the center of the beam (lb/ft).
■
EXAMPLE 11.16
Problem
: A 10-ton hoist is suspended at the midpoint of a beam that is supported at each end. What
would the design basis need to be for these supports if we specified a safety factor of 4?
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