CEE 220 1
Homework Assignment No. 2 Solution
Following the homework presentation guidelines listed in the syllabus, prepare solutions to
the following problems. For all problems, write a problem statement, provide sketches, and
comment on your thought processes. Draw free-body diagrams for each component of a
problem as applicable.
1. Bolted Connection
Consider the cover-plate beam, bolted connection shown in figures. P is 700 kips and
there are two lines of two bolts in each flange.
(a) Under what circumstances can we assume each bolt carries an equal portion of
the load?
(b) Determine the maximum shear force in each bolt assuming equal load distribution.
(c) Determine the required diameter of the bolts such that the allowable shear stress
is not exceeded. Use a failure shear stress of τf ail = 68 ksi and a factor of safety
for shear of 1.6.
Hint: The allowable shear stress is not the failure shear stress, but is related to
this value.
Solution
(a) For each bolt to carry an equal portion of the load both plates must have equal
stiffness which occurs when they deflect the same amount under loading. This means
AE
that the ratio is the same for both plates. This is usually caused by both plates
L
having the same exact properties.
(b) The 3” dimensions are included to show that the 70 kip force acts at the center of
both plates and equal distance from all four rows of bolts. Therefore, the forces in all
8 bolts are equal.
,CEE 220 2
Free body diagram for of top plate:
P 700
Maximum shear force per bolt, V = = = 87.5k
#Bolts 8
τf ail 68Ksi
(c) τallow = = = 42.5 ksi
F.S 1.6
V 87.5
τ= ≤ τallow → π ≤ 42.5
A d2
v 4
u 87.5 5
d ≥ tπ → d ≥ 1.62” = 1 ”ϕ
u
42.5 8
4
, CEE 220 3
2. Axial Joint Consider the compression member shown in the figure. The member
has a 3-inch square cross and carries an axial force of P = 1.5 kips. The member is
constructed of two components that are glued together as shown in figure.
(a) Determine the normal force, N , on the plane of the glue.
(b) Determine the shear force, V , on the plane of the glue.
(c) Determine the average normal stress on the plane of the glue.
(d) Determine the average shear stress on the plane of the glue.
(e) Determine the maximum allowed applied compression force, P , if the allowable
stress of the glue is 0.2 ksi in compression and 0.05 ksi in shear.
Solution
We can cut the member along the inclined plane and perform our statics equations to
find the forces along the cut that provide equilibrium to the system. To find the
stresses we divide the shear and normal force over the section area. This gives us the
following answers for parts (a) through (d):
Homework Assignment No. 2 Solution
Following the homework presentation guidelines listed in the syllabus, prepare solutions to
the following problems. For all problems, write a problem statement, provide sketches, and
comment on your thought processes. Draw free-body diagrams for each component of a
problem as applicable.
1. Bolted Connection
Consider the cover-plate beam, bolted connection shown in figures. P is 700 kips and
there are two lines of two bolts in each flange.
(a) Under what circumstances can we assume each bolt carries an equal portion of
the load?
(b) Determine the maximum shear force in each bolt assuming equal load distribution.
(c) Determine the required diameter of the bolts such that the allowable shear stress
is not exceeded. Use a failure shear stress of τf ail = 68 ksi and a factor of safety
for shear of 1.6.
Hint: The allowable shear stress is not the failure shear stress, but is related to
this value.
Solution
(a) For each bolt to carry an equal portion of the load both plates must have equal
stiffness which occurs when they deflect the same amount under loading. This means
AE
that the ratio is the same for both plates. This is usually caused by both plates
L
having the same exact properties.
(b) The 3” dimensions are included to show that the 70 kip force acts at the center of
both plates and equal distance from all four rows of bolts. Therefore, the forces in all
8 bolts are equal.
,CEE 220 2
Free body diagram for of top plate:
P 700
Maximum shear force per bolt, V = = = 87.5k
#Bolts 8
τf ail 68Ksi
(c) τallow = = = 42.5 ksi
F.S 1.6
V 87.5
τ= ≤ τallow → π ≤ 42.5
A d2
v 4
u 87.5 5
d ≥ tπ → d ≥ 1.62” = 1 ”ϕ
u
42.5 8
4
, CEE 220 3
2. Axial Joint Consider the compression member shown in the figure. The member
has a 3-inch square cross and carries an axial force of P = 1.5 kips. The member is
constructed of two components that are glued together as shown in figure.
(a) Determine the normal force, N , on the plane of the glue.
(b) Determine the shear force, V , on the plane of the glue.
(c) Determine the average normal stress on the plane of the glue.
(d) Determine the average shear stress on the plane of the glue.
(e) Determine the maximum allowed applied compression force, P , if the allowable
stress of the glue is 0.2 ksi in compression and 0.05 ksi in shear.
Solution
We can cut the member along the inclined plane and perform our statics equations to
find the forces along the cut that provide equilibrium to the system. To find the
stresses we divide the shear and normal force over the section area. This gives us the
following answers for parts (a) through (d):
