A Beginner's Guide to the Steel Construction Manual, 14th ed.

Chapter 3 - Tension Members

2006, 2007, 2008, 2011 T. Bartlett Quimby

Overview

Slenderness

Tensile Yielding

Tensile Rupture

Failure Path Tutorial

Tensile Yielding & Tensile Rupture of Connecting Elements

Bolt Bearing on Holes

Block Shear

Selecting Sections

Tension Limit State Summary

Example Problems

Homework Problems

References


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Section 3.11

Homework Problems

Last Revised: 07/30/2011

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            
2            
1            
P & R 3            
2            
1            
11 A & B 3            
2            
1            
P & R 3            
2            
1            

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        
G        
F        
E        
D        
C        
B        
A        

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    
2-5    
5-3    

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