Section 3.11
Homework Problems
Last Revised:
06/16/2011
The
homework problems involve the design of elements of three different structures
plus some unrelated details. Please see the relevant links below for each
structure. When completing the problems, consider both ASD and LRFD design
philosophies unless otherwise specified by the instructor. Consider all
limit states presented in this chapter. Consider developing a generic
spreadsheet that you can apply to similar problems.
Miscellaneous Problems
Problems M3.1: Use the connection drawing MISCDET 1/S1.2
for all
3.1.x problems. Assume that the connection is subjected to a
tensile force that consists of one part wind load, 2 parts dead load,
and 2.5 parts live load.
Problem M3.1.1: Determine the tensile strength (at
service load levels) of the connection based on the capacity the pair of the
side plates.
LRFD (service level capacity) = _____________
ASD (service level capacity) = _____________
Problem M3.1.2: Determine the tensile strength (at service
load levels) of the connection based on the capacity of the center
plate.
LRFD (service level capacity) = _____________
ASD (service level capacity) = _____________
Problems M3.2: Use the connection drawing MISCDET 5/S1.1 for all
3.2.x problems. Assume that the applied load will consist of equal
magnitude dead, live, and seismic loads.
Problem M3.2.1: Determine the tensile strength (at service
load levels) of the connection based on the capacity of a pair of
the channels.
LRFD (service level capacity) = _____________
ASD (service level capacity) = _____________
Problem M3.2.2: Select the thickness of the connecting splice plate so that it has
sufficient strength to carry the following loads: D = 100 k, L = 150 k, W = 200
k, E = 250 k. Specify the plate thickness to the nearest 1/16" that
satisfies the criteria.
tpl = _________________
Problem M3.3: Use the connection drawing MISCDET 3/S2.1 for all
3.3.x problems. Assume that the applied load will consist of equal
magnitude dead, live, and seismic loads. The angles are L5x5x3/8"
and the gusset plate is 7/16" thick. The dimensions are: A =
1.5", B = 2", X = 7, and C = 2". Consider, and report the
capacities of all applicable limit states covered in this chapter for
each problem.
Problem M3.3.1: Determine the tensile strength (at service
load levels) of the connection based on the capacity of a pair of
the angles.
LRFD (service level capacity) = _____________
ASD (service level capacity) = _____________
Problem M3.3.2: Determine the block shear strength (at
service load levels) of the gusset plate.
LRFD (service level capacity) = _____________
ASD (service level capacity) = _____________
Problem M3.4: Use the connection drawing MISCDET 4/S1.2 for all
3.4.x
problems. Ignore any connection eccentricity. Consider, and report
the capacities of all applicable limit states covered in this chapter for each
problem.
Problem M3.4.1: Determine the axial tensile capacity (both LRFD,
fTn, and ASD, Tn/W)
of the WTs.
fTn, = ________________,
Controlling Limit State: _________________
Tn/W = _________________,
Controlling Limit State: _________________
Problem M3.4.2: Determine the axial tensile capacity (both LRFD,
fTn, and ASD, Tn/W)
of the connection based on the capacity of the connection plates.
fTn, = ________________,
Controlling Limit State: _________________
Tn/W = _________________,
Controlling Limit State: _________________
Dormitory Building Design Problems
The braces for this building are both tension and compression members, depending
on the direction of lateral forces. For this chapter, we will design them
based on their tensile capacity. Later, we will revisit the design of
these members as compression members. See drawings
BLDG 4/S3 and BLDG 5/S3 for the
following problems.
Problem D3.1: Select a section for the brace on the first
floor level on Grid 2 and between Grids A & B. For members with
bolted connections determine the required number of bolts to satisfy the
limit state of bolt bearing on holes. Using the required number of
bolts, neatly sketch to scale the layout out of the bolts that you use to
compute the tensile rupture and block shear limit states for the member you
selected.
- D3.1a: Select the lightest single channel for this
member. The connection is similar to MISCDET 1/S2.1 (instead
of two channels, use one). In the referenced detail, use A > 1.5" and
B > 3" for this problem.
- D3.1b: Select the lightest double angle section for
this member. If the connected leg is wider than 5", assume
that the member has a double gage line of bolts as shown in drawing
MISC 3/S2.1, otherwise assume that there is a single line of bolts.
Center the bolt group on the connected angle leg. In the
referenced detail use A > 1.5", B = 2.0", and C = 3" for this
problem.
- D3.1c: Select the lightest square HSS section for
this member. Assume that the ends of the section are slotted
to accommodate a 1/2" thick connection plate similar to that shown
on drawing MISCDET 5/S2.1. For now, assume that the connecting
welds are each 10 inches long. (i.e. the lap of the member with the
gusset plate is 10".)
Problem D3.2: Repeat Problem D3.1 for the other braces in
the structure. Complete the following table by adding the lightest
member sizes that satisfy the criteria:
On Grid |
Between Grids |
Level |
Problem # |
D3.2a |
D3.2b |
D3.2c |
Square HSS |
Dble Angle |
Single Channel |
ASD |
LRFD |
ASD |
LRFD |
ASD |
LRFD |
2 |
A & B |
3 |
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2 |
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1 |
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P & R |
3 |
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2 |
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1 |
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11 |
A & B |
3 |
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2 |
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1 |
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P & R |
3 |
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2 |
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1 |
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Tower Design Problems
The tower is made of members that are all axial force members. All the
members have one or more load conditions that exert axial tension and
compression on the members. For this part of the design, we will only
consider the tension forces. In this truss structure, it is possible to
analyze the structure so in such a way that axial compression is not allowed in
the diagonal members, making them tension only. This is a conservative
approach that often allows smaller members to be used. The table of member
forces found in the drawing set are based on the diagonals being tension only
members.
Problem T3.1: Select a member for a diagonal brace at level
"A". For members with bolted connections determine the required number
of bolts to satisfy the limit state of bolt bearing on holes. Using
the required number of bolts, neatly sketch to scale the end of the member
showing the layout out of the
bolts that you use to compute the tensile rupture and block shear limit
states for the member you selected.
- T3.1a: Select the lightest single angle. Assume a
single line of bolts along the axis of the member connects the angle to
tower leg similar to the detail shown in TOWER 3/S2.
- T3.1b: Select the lightest round HSS section.
Assume that the member is slotted to accommodate a 3/8" thick gusset
plate similar to the connection shown in TOWER 3/S3. Assume that
the lap length of the HSS and the gusset plate equals the HSS diameter,
D.
Problem T3.2: Select a member for the diagonal braces at the
other levels of the tower. Provide neatly drawing scaled sketches of
the member ends detailing the bolt patterns. Complete the following
table by adding the lightest sections that satisfy the criteria.
- T3.2a: Select the lightest single angle. Assume a
single line of bolts along the axis of the member connects the angle to
tower leg similar to the detail shown in TOWER 3/S2.
- T3.2b: Select the lightest round HSS section.
Assume that the member is slotted to accommodate a 3/8" thick gusset
plate similar to the connection shown in TOWER 3/S3. Assume that
the lap length of the HSS and the gusset plate equals the HSS diameter,
D.
Level |
Problem # |
T3.2a |
T3.2b |
Single Angle |
Rnd HSS |
ASD |
LRFD |
ASD |
LRFD |
H |
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G |
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F |
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E |
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D |
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C |
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B |
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A |
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Problem T3.3: Select a round HSS section
for the segment 1 of a typical tower leg. The end connections are
similar to that shown in TOWER 2/S2.
Truss Bridge Design Problems
The bridge is a truss, so all the members in the side trusses are essentially
axial force members. The member forces can be found in the drawing set.
Threat the vehicle loading like a floor live load and the ice loading as a snow
load for the purposes of these problems.
Problem B3.1: Select the one lightest section from the W8,
W10, and W12 categories for use as member 3-4 of the truss. This is
the central bottom chord member and its flanges are connected to a pair of
gusset plates as shown in TBRDG 3/S5. Determine the required number
of bolts to satisfy the limit state of bolt bearing on holes. Using
the required number of bolts, neatly sketch to scale the layout out of the
bolts that you use to compute the tensile rupture and block shear limit
states for the member you selected.
Problem B3.2: Repeat problem B3.1 for each of the other
tension members in the truss. All members need to be the same nominal
depth (i.e. they must all be either W8s or W10s or W12s) in order for the
members to fit together properly. Complete the following table with
the best choices for each member:
Member |
Member Size |
ASD |
LRFD |
1-2-3 |
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|
2-5 |
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|
5-3 |
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