383
Ans:
4–151.
SOLUTION
Equivalent Resultant Force:
Location of Equivalent Resultant Force:
O
7.5 m 4.5 m
500 kN m
6kN/m15 kN
Replace the loading by a single resultant force, and specify
the location of the force measured from point O.
384
SOLUTION
Equivalent Resultant Force And Couple Moment At Point A. Summing the forces
along the y axis by referring to Fig. a,
*4–152.
Replace the loading by an equivalent resultant force and
couple moment acting at point A.
AB
3 m
400 N/m
3 m
385
Ans:
SOLUTION
Equivalent Resultant Force. Summing the forces along the y axis by referring
toFig.a,
Location of Resultant Force. Summing the moment about point A by referring
4–153.
Replace the loading by a single resultant force, and specify
its location on the beam measured from point A.
AB
3 m
400 N/m
3 m
386
SOLUTION
Equivalent Resultant Force. Summing the forces along the x and y axes by referring
to Fig. a,
Location of the Resultant Force. Summing the moments about point A, by referring
to Fig. a,
4–154.
Replace the distributed loading by an equivalent resultant
force and specify where its line of action intersects a
horizontal line along member AB, measured from A.
4 m
3 kN/m
2 kN/m
3 m
A
B
C
387
Ans:
4–154. Continued
388
4–155.
Replace the distributed loading by an equivalent resultant
force and specify where its line of action intersects a vertical
line along member BC, measured from C.
4 m
3 kN/m
2 kN/m
3 m
A
B
C
SOLUTION
Equivalent Resultant Force. Summing the forces along the x and y axes by referring
to Fig. a,
Location of the Resultant Force. Summing the moments about point A, by referring
to Fig. a,
389
Ans:
4–155. Continued
390
Ans:
SOLUTION
Equivalent Resultant Force And Couple Moment At Point A. Summing the forces
*4–156.
Determine the length b of the triangular load and its
position a on the beam such that the equivalent resultant
force is zero and the resultant couple moment is 8 kN
#
m
clockwise.
4 m
b
a
6 kN/m
2 kN/m
A
391
Ans:
SOLUTION
Equivalent Resultant Force And Couple Moment About Point O. The differential
Summing the moments about point O,
4–157.
Determine the equivalent resultant force and couple
moment at point O.
w
w ( x3 ) kN/m
9 kN/m
1
3
x
O
3 m
392
Ans:
4–158.
SOLUTION
Determine the magnitude of the equivalent
resultant force and its location, measured from
point O.
O
w
6 ft
4 lb/ft
8.90 lb/ft
x
w (4 2 x ) lb/ft
393
SOLUTION
4–159.
The distributed load acts on the shaft as shown. Determine
the magnitude of the equivalent resultant force and specify
its location, measured from the support, A.
10 lb/ft
28 lb/ft
AB
w
x
18 lb/ft
w (2x¤ 8x 18) lb/ft
1 ft 2 ft 2 ft
394
Ans:
*4–160.
Replace the distributed loading with an equivalent resultant
force, and specify its location on the beam measured from
point A.
SOLUTION
Resultant:The magnitude of the differential force is equal to the area of the ele-
ment shown shaded in Fig.a.Thus,
Location:The location of on the beam is measured from point A.Thus,
the location of measured from point Ais given by
FR
x
xc=xdFR
dFR
100 lb/ft
15 ft
370 lb/ft
w
A
B
x
w (x2 3x 100) lb/ft
395
SOLUTION
Summing the moments about point O,
4–161.
Replace the loading by an equivalent resultant force and
couple moment acting at point O.
L
Ox
w
w w0 cos x
2L
p
(
(
396
Ans:
4–162.
Wet concrete exerts a pressure distribution along the wall
of the form. Determine the resultant force of this
distribution and specify the height hwhere the bracing strut
should be placed so that it lies through the line of action of
the resultant force.The wall has a width of 5 m.
4m
h
(4 ) kPa
p
1/2
z
8 kPa
p
SOLUTION
Equivalent Resultant Force:
Location of Equivalent Resultant Force:
:
+FR=©Fx;–FR=-
LdA =-
Lz
0
w
dz