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Section 4.10
Homework Problems
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 and prior chapters. Consider developing a generic
spreadsheet that you can apply to similar problems.
Miscellaneous Steel Problems
Problem M4.1: For this problem, use
the two W sections in tension that are
connected together as shown in drawing MISCDET_STL 1/S1.1. Express your results in terms of service load levels assuming
that the applied load is 1 part dead load, 1.5 parts live load, and 0.75 part
seismic load.
- M4.1a: Determine the capacity of the connection
based on the slip capacity (as a "slip critical" connection) provided by the
bolts. In other words, the bolts are "-SC" bolts. Assume a Class
A surface on the plates.
- M4.1b: Determine the
capacity of the connection based on bolt strength (a "bearing" type
connection).
Problems M4.2.x: For this problem, neglect any load eccentricity.
Express your results in terms of service load levels assuming
that the applied load is 1 part dead load, 1.5 parts live load, and 1.25 part
wind load.
Problem M4.2.1: Use the connection shown on drawing MISCDET_STL
1/S1.2
- M4.2.1.a: Determine the capacity of the
connection based on bolt strength (a "bearing" type connection) if the
bolt threads are included in the shear planes.
- M4.2.1.b: Determine the capacity of the
connection based on the slip capacity (as a "slip critical" connection)
provided by the bolts. In other words, the bolts are "-SC" bolts.
Assume a Class A surface on the plates.
Problem M4.2.2: Use the connection shown on drawing MISCDET_STL
4/S1.2.
- M4.2.2.a: Determine the capacity of the
connection based on bolt strength (a "bearing" type connection) if the
bolt threads are not included in the shear planes.
- M4.2.2.b: Determine the capacity of the
connection based on the slip capacity (as a "slip critical" connection)
provided by the bolts. In other words, the bolts are "-SC" bolts.
Assume a Class A surface on the plates.
Problem M4.3: For this problem refer to drawing MISCDET_STL 3/S1.1.
Two pipe sections are connected by steel flanges as shown. Determine the tension that can be applied to the pipe without
exceeding the tensile capacity of the bolts. Express
your results in terms of service load levels assuming that the applied load is 1
part dead load, 1 part live load, 1.5 part seismic load, and 1.25 part wind
load.
Problem M4.4: For this problem refer to drawing MISCDET_STL 1/S5.1. Create a general purpose spreadsheet (in MS Excel unless otherwise
approved by your instructor) to compute the capacity, Pn for the
eight bolt connection shown. Consider only bolt strength (i.e. type -N and
-X bolts). The design variables are the spacing between rows (Y), the
distance between columns (Z), the location of the force (X), the angle of
loading (Angle) from the vertical, and the bolt size and type information.
Group the design variables and the resulting value at the beginning of the
spreadsheet.
- M4.4a: Use the elastic vector method
- M4.4b: Use the IC method
Problem M4.5: For this problem refer to drawing
MISCDET_STL 2/S5.1. Create a general purpose spreadsheet (in MS Excel unless otherwise
approved by your instructor) to compute the capacity, Pn for the ten
bolt connection shown. Consider only bolt strength (i.e. type -N and -X
bolts). The design variables are the sizes of the WT and W section, the spacing between rows (Y), the
distance between columns (Z), the location of the force (X), and the bolt size
and type information. Group the design variables and the resulting value
at the beginning of the spreadsheet.
Suggestion: write your spreadsheet to input a given factored load (Pu
or Pa) then compute the values of the applicable limit states.
Use goal seek on the factored load until the controlling
limit state is maxed out.
- M4.5a: Use the AISC Case I method
- M4.5b: Use the AISC Case II method.
Problem M4.6: Drawing MISCDET_STL 2/S1.1 shows a splice connection for a pair
of W sections. This connection is capable of resisting moment by a couple
that forms in the opposing flange plates (one plate in axial compression and the
other one in axial tension). All the force in the flange plates must be
transferred to the flanges of the beam via the bolts. Based on bolt
strength only, what is the maximum nominal moment (Mn = Pn
* dist between plate centers) that the connection can resist? The W
section is a W18x35, D=6", the plates are 1/2" thick, and the bolts
are 3/4" diameter A490-SC bolts.
Dormitory Building Design Problems
The braces in this building may be connected to the frames by bolts, depending
on the detail used. In these problems, the connections will be designed
based on bolt strength and/or slip resistance.
Problem D4.1: For a brace on the first
floor level on Grid 2 and between Grids A & B determine the required number of bolts to satisfy the
limit state of bolt capacity. Assume that the brace consists of a pair
of angles as shown in MISCDET_STL 3/S2.1.
- D4.1a: Determine the required number of bolts based on bolt strength
if threads are excluded from the shear plane.
- D4.1b: Determine the required number of bolts based on bolt
strength if threads are not excluded from the shear plane
- D4.1c: Determine the required number of bolts based on slip
strength.
Problem D4.2: Repeat Problem D4.1 for the other braces in
the structure. Complete the following table by adding the best choice
for each member:
| On Grid |
Between Grids |
Level |
Problem # |
| D4.2a |
D4.2b |
D4.2c |
| Thread Excluded |
Threads Included |
Slip Critical |
| ASD |
LRFD |
ASD |
LRFD |
ASD |
LRFD |
| 2 |
A & B |
3 |
|
|
|
|
|
|
| 2 |
|
|
|
|
|
|
| 1 |
|
|
|
|
|
|
| P & R |
3 |
|
|
|
|
|
|
| 2 |
|
|
|
|
|
|
| 1 |
|
|
|
|
|
|
| 11 |
A & B |
3 |
|
|
|
|
|
|
| 2 |
|
|
|
|
|
|
| 1 |
|
|
|
|
|
|
| P & R |
3 |
|
|
|
|
|
|
| 2 |
|
|
|
|
|
|
| 1 |
|
|
|
|
|
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Problem D4.3: A beam to column connection similar to that
shown in MISCDET_STL 1/S3.1 (A = 3", B = 5", C = 1.1/2", and D = 2.5") is to be
used to connect the second floor beam on grid C between grids 3 & 6 (See the
floor framing plan on DORM S1) to the columns at either end of the beams.
The beam supports 3'-4" of the corridor on one side and 6'-3" of dorm room
on the other along it's length. It also supports a 10 ft tall interior
wall along it's length. Compute the reactions for the beam then select
the number of "-N" bolts required to connect the WT to the column.
Neatly sketch a detail of the bolt layout.
- D4.3a: Select the bolts using AISC Case I method.
- D4.3b: Select the bolts using AISC Case II method.
Tower Design Problems
The tower diagonal braces are bolted to the tower legs. Since towers are
subjected to frequently reversing loads, all connections are to be designed as
slip critical connections.
Problem T4.1: Determine the number of bolts required for a
brace at level A of the tower.
- T4.1a: Assuming a single gage line of bolts on a single
angle, neatly draw a scaled detail of the end of the brace showing the
bolt layout. Minimize the length of the connection. The
connection is to be similar to TOWER 4/S2.
- T4.1b: Assuming the bolts connect an end plate of a
tubular member to the gusset plate similar that shown in TOWER 4/S3.
Neatly draw a scaled detail of the end of the brace showing the bolt
layout. Minimize the length of the connection.
Problem T4.2: Repeat problem T4.1 for each level of the
tower. Complete the following table by filling in the required number
of bolts at each level.
| Level |
Req'd # of Bolts |
| T4.2a |
T4.2b |
| ASD |
LRFD |
ASD |
LRFD |
| H |
|
|
|
|
| G |
|
|
|
|
| F |
|
|
|
|
| E |
|
|
|
|
| D |
|
|
|
|
| C |
|
|
|
|
| B |
|
|
|
|
| A |
|
|
|
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Problem T4.3: Select the number of bolts
needed to connect tower leg segment 1 to tower leg segment 2 as shown in
TOWER 2/S2.
Truss Bridge Design Problems
The bridge has all bolted connections. Since none of the members have
reversing loads, we can use bearing type connections.
Problem B4.1: Determine the number of bolts
needed to connect member 3-4 to the gusset plates a Joint type 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. Using
the required number of bolts, neatly sketch to scale the layout out of the
bolts that you selected.
Problem B4.2: Repeat problem B4.1 for each of the other
members in the truss. Complete the following table by adding the
required number of bolts in each case:
| Member |
# of bolts at each end |
| ASD |
LRFD |
| 1-2-3 |
|
|
| 1-5 |
|
|
| 2-5 |
|
|
| 3-4 |
|
|
| 3-7 |
|
|
| 4-7 |
|
|
| 5-3 |
|
|
| 5-6-7 |
|
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Problem B4.3: A typical girder is connected to a
vertical via a pair of connection angles as shown in TBRDG 2/S4 and TBRDG
4/S4. The girder reaction consists of 40.5 kips vehicle load, 23.0 kips
dead load, and 2.20 kips of ice load.
-
B4.3a: Determine the required
number of bolts to connect the girder web to the pair of connection
angles. Neatly sketch to scale the bolt layout if the girder
is 27" deep.
-
B4.3b: Determine the required
number of bolts to connect the connection angles to the vertical.
Assume that the load eccentricity is 5" from the face of the
vertical.
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