PROBLEM 5.67
For the beam and loading shown, determine (a) the
magnitude and location of the resultant of the
distributed load, (b) the reactions at the beam supports.
SOLUTION
(a)
RI
RII
R
1
(1100 N/m) (6 m) 2200 N
3
(900 N/m) (6 m) 5400 N
RI
RII
2200 5400 7600 N
XR
xR :
X
2.5658 m
MA
(b)
X (7600)
(2200)(1.5) (5400)(3)
R
7.60 kN ,
X
2.57 m
0: B (6 m) (7600 N)(2.5658 m) 0
B 3250.0 N
B 3.25 kN
Fy
0: A 3250.0 N 7600 N
A
0
4350.0 N
A
4.35 kN
Copyright © McGraw-Hill Education. Permission required for reproduction or display.
PROBLEM 5.69
Determine the reactions at the beam supports for the given
loading.
SOLUTION
RI
RII
1
(50 lb/in.)(12 in.)
2
300 lb
(50 lb/in.)(20in.)
1000 lb
Fy
0: Ay
300 lb 1000 lb 400 lb 0
A 900 lb
MA
0: M A
(300 lb)(8 in.) (1000 lb)(22 in.)
400 lb 38 in.
0
MA
9200 lb in.
Copyright © McGraw-Hill Education. Permission required for reproduction or display.
PROBLEM 5.76
Determine the reactions at the beam supports for the given
loading when wO 400 lb/ft.
SOLUTION
1
1
wO (12 ft)
(400 lb/ft)(12 ft)
2
2
1
(300 lb/ft)(12 ft) 1800 lb
2
RI
RII
MB
C
Fy
B
2400 lb
0: (2400 lb)(1 ft) (1800 lb)(3 ft) C (7 ft)
428.57 lb
0
C 429 lb
0: B 428.57 lb 2400 lb 1800 lb 0
3771 lb
B
3770 lb
Copyright © McGraw-Hill Education. Permission required for reproduction or display.
PROBLEM 5.78
The beam AB supports two concentrated loads and rests on soil that
exerts a linearly distributed upward load as shown. Determine the
values of A and B corresponding to equilibrium.
SOLUTION
RI
RII
MD
For a
1
2
1
2
A (1.8
m) 0.9
A
B (1.8
m) 0.9
B
0: (24 kN)(1.2 a ) (30 kN)(0.3 m) (0.9
0.6 m,
A )(0.6
m)
24(1.2 0.6) (30)(0.3) 0.54
14.4 9 0.54
Fy
0:
A
0
24 kN 30 kN 0.9(10 kN/m) 0.9
a
A
B
0
B
0
0
10.00 kN/m
50.0 kN/m
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