PROBLEM 12.2
For the beam and loading shown, (a) draw the shear and bending–moment
diagrams, (b) determine the equations of the shear and bending–moment
consent of McGraw–Hill Education.
PROBLEM 12.3
For the beam and loading shown, (a) draw the shear and bending–moment
diagrams, (b) determine the equations of the shear and bending–moment
curves.
PROBLEM 12.4
For the beam and loading shown, (a) draw the shear and bending–moment
diagrams, (b) determine the equations of the shear and bending–moment
curves.
SOLUTION
Calculate reactions after replacing distributed load by an equivalent
concentrated load.
PROBLEM 12.4 (Continued)
From C to D:
La x L
−<<
1
0: ( 2 ) 0
2
y
F V wL aΣ= + − =
( 2)
2
w
V La
=−−
1
0: ( 2 )( ) 0
2
J
M M wL a L xΣ = −+ − − =
1( 2 )( )
2
M wL a L x= −−
At
,
2
L
x=
22
max
82
La
Mw
= −
consent of McGraw–Hill Education.
PROBLEM 12.5
Draw the shear and bending-moment diagrams for the beam and loading
shown, and determine the maximum absolute value (a) of the shear,
(b) of the bending moment.
SOLUTION
PROBLEM 12.5 (Continued)
(a)
max
430 lb
V=
(b)
max
1200 lb inM= ⋅
consent of McGraw–Hill Education.
PROBLEM 12.6
Draw the shear and bending–moment diagrams for the beam and
loading shown, and determine the maximum absolute value (a) of the
shear, (b) of the bending moment.
SOLUTION
At B,
200N, 0VM= =
+
PROBLEM 12.6 (Continued)
At A,
0 : 200 200 500 200 0 100 N
y
FV V∑= −−+−= =
0 : (0.3)(200) (0.525)(200) (0.825)(500) (1.05)(200) 0
37.5 N m
A
MM
M
∑ = −− − + − =
= ⋅
consent of McGraw–Hill Education.
PROBLEM 12.7
Draw the shear and bending–moment diagrams for the beam and loading
shown, and determine the maximum absolute value (a) of the shear,
(b) of the bending moment.
SOLUTION
PROBLEM 12.2
For the beam and loading shown, (a) draw the shear and bending–moment
diagrams, (b) determine the equations of the shear and bending–moment
consent of McGraw–Hill Education.
PROBLEM 12.3
For the beam and loading shown, (a) draw the shear and bending–moment
diagrams, (b) determine the equations of the shear and bending–moment
curves.
PROBLEM 12.4
For the beam and loading shown, (a) draw the shear and bending–moment
diagrams, (b) determine the equations of the shear and bending–moment
curves.
SOLUTION
Calculate reactions after replacing distributed load by an equivalent
concentrated load.
PROBLEM 12.4 (Continued)
From C to D:
La x L
−<<
1
0: ( 2 ) 0
2
y
F V wL aΣ= + − =
( 2)
2
w
V La
=−−
1
0: ( 2 )( ) 0
2
J
M M wL a L xΣ = −+ − − =
1( 2 )( )
2
M wL a L x= −−
At
,
2
L
x=
22
max
82
La
Mw
= −
consent of McGraw–Hill Education.
PROBLEM 12.5
Draw the shear and bending-moment diagrams for the beam and loading
shown, and determine the maximum absolute value (a) of the shear,
(b) of the bending moment.
SOLUTION
PROBLEM 12.5 (Continued)
(a)
max
430 lb
V=
(b)
max
1200 lb inM= ⋅
consent of McGraw–Hill Education.
PROBLEM 12.6
Draw the shear and bending–moment diagrams for the beam and
loading shown, and determine the maximum absolute value (a) of the
shear, (b) of the bending moment.
SOLUTION
At B,
200N, 0VM= =
+
PROBLEM 12.6 (Continued)
At A,
0 : 200 200 500 200 0 100 N
y
FV V∑= −−+−= =
0 : (0.3)(200) (0.525)(200) (0.825)(500) (1.05)(200) 0
37.5 N m
A
MM
M
∑ = −− − + − =
= ⋅
consent of McGraw–Hill Education.
PROBLEM 12.7
Draw the shear and bending–moment diagrams for the beam and loading
shown, and determine the maximum absolute value (a) of the shear,
(b) of the bending moment.
SOLUTION