Buckling Packet

This packet is intended for use in a mechanical engineering Strength of Materials course. The buckling module should be used after the students have learned buckling. This module touches on the concept of designing for assembly, namely buckling in bridges under construction. Factors to be considered in design are discussed. An example of a bridge that collapsed while under construction is presented, as is a homework problem dealing with a bridge truss. Sample exam problems are included.

Time for presentation is estimated as 25-30 minutes.

Objectives:

1. To gain an increased understanding of safety in design.

2. To further develop knowledge of buckling.

3. To recognize the importance of designing for assembly.

This packet includes the following items:

•Lecture material for the instructor

•Overheads for use during the lecture

•Handouts for the students

•Homework problem

Download the Buckling packet in a printable Adobe Acrobat Format (pdf).  This includes overheads in a ready to use format.

Homework problem solutions, exam problems, and exam solutions are available to qualified recipients. Send an email with request information to Dr. Donald Bloswick.

Buckling Lecture Outline

1. Designing for Assembly (OVERHEAD 1)
1. Engineers are responsible for their designs in all stages of product life, including during construction, continuing through the life of the structure, and disposal once the system becomes obsolete.
2. Engineers must be aware of loading requirements and evolving material properties when designing and account for the life cycle requirements.
3. (OVERHEAD 2) Buckling is an issue that must be dealt with in the design phase.
1. Even though a structure is designed to be stable in the final form, it must also be resistant to buckling while in transit and under construction.
2. Buckling is mostly a function of the length-to-width ratio for members under axial compressive loading. Under such conditions, pure compression failure is rare in materials like concrete or steel.
3. As discussed in class, cross-sectional area, excessive unsupported length, and the modulus of elasticity of the material also play important roles. Yield strength is not an issue in pure buckling.
4. (OVERHEAD 3) An example of buckling while a structure is under construction may occur when bridges are being fabricated.
5. When a bridge is under construction, some members might be in compression that were designed to withstand tensile forces during service. Unless this condition is considered during design, members may buckle, causing the structure to fail during construction.
6. (OVERHEAD 4) During bridge construction, many factors must be considered, including
1. bridge span weight distribution,
2. wind forces,
3. temperature effects,
4. and other stresses, some acting in combination.
7. Due to the many unknowns, higher safety factors may be needed to reduce the chance of buckling.
2. West Gate Bridge (OVERHEAD 5)
1. The West Gate Bridge, built in Melbourne, Australia, collapsed during construction in October 1970.
1. At the time, the British safety factor for bridges was 1.70 (Ross, 177), based on usage allowable loading. However, for construction, the safety factor was only 1.31.
2. (OVERHEAD 6) The full length bridge was to be five spans of cable-stayed steel box girders, with support given by prestressed concrete approach viaducts. The bridge was 8500 feet in length.
1. Underneath the section of the bridge that collapsed were site huts. Approximately 35 people were killed and many others were injured.
2. The engineers who designed the bridge had a previous collapse during another bridge construction effort.
3. Because of the West Gate Bridge collapse, the bridge designers were forced to redesign the bridge.
2. Causes of the West Gate Bridge Collapse (OVERHEAD 7)
1. The main cause of the bridge collapse was the removal of bolts in order to join sections of the bridge together.
2. Portions of the bridge were preassembled on the ground.
3. As one of the sections was being lifted, some bridge members buckled. It was thought that the buckled section could be repaired when in place.
4. As the next section was brought into place, the sections could not be connected due to buckling in the previous section.
5. Various methods were used to try to bring the sections into alignment, but buckling of the entire structure occurred.
6. Temporary support structures were used during construction, as well as hydraulic jacks.
7. Engineers in charge of this project assumed a symmetric structure, instead of asymmetric, as the bridge was constructed. This assumption made the calculations incorrect, and consequently contributed to the buckling.
8. The circumstances of this collapse were very complex, but ultimately the designer's mistakes led to buckling.
3. Conclusion (OVERHEAD 8)
1. Engineers are ultimately responsible for their designs and the resulting consequences.
2. Loading requirements and evolving material properties throughout the life-cycle of the system are important elements to be considered in design.
3. Buckling is a very important failure mode to consider for applications where the structure is not as stable during construction as it is in its finished form.

1980.

Ross, Steven S. Construction Disasters: Design Failures, Causes, and Prevention. New York: McGraw-Hill, Inc., 1984.

Buckling

Overhead 1

Designing for Assembly

Engineers are responsible for their designs in all stages of product life, including during construction, continuing through the life of the structure, and disposal once the system becomes obsolete.

Engineers must be aware of loading requirements and evolving material properties when designing and account for the life cycle requirements.

Overhead 2

Buckling is an issue that must be dealt with in the design phase

•Even though a structure is designed to be stable in the final form, it must also be resistant to buckling while in transit and under construction.

•Buckling is mostly a function of the length-to-width ratio for members under axial compressive loading. Under such conditions, pure compression failure is rare in materials like concrete or steel.

•As discussed in class, cross-sectional area, excessive unsupported length, and the modulus of elasticity of the material also play important roles. Yield strength is not an issue in pure buckling.

---

Overhead 3

An example of buckling while a structure is under construction may occur when bridges are being fabricated.

When a bridge is under construction, some members might be in compression that were designed to withstand tensile forces during service. Unless this condition is considered during design, members may buckle, causing the structure to fail during construction.

Overhead 4

During bridge construction, many factors must be considered, including

•bridge span weight distribution,

•wind forces,

•temperature effects,

•and other stresses, some acting in combination.

Due to the many unknowns, higher safety factors may be needed to reduce the chance of buckling.

Overhead 5

West Gate Bridge

The West Gate Bridge, built in Melbourne, Australia, collapsed during construction in October 1970.

At the time, the British safety factor for bridges was 1.70 based on usage allowable loading. However, for construction, the safety factor was only 1.31.

Overhead 6

The full length bridge was to be five spans of cable-stayed steel box girders, with support given by prestressed concrete approach viaducts. The bridge was 8500 feet in length.

•Underneath the section of the bridge that collapsed were site huts. Approximately 35 people were killed and many other were injured.

•The engineers who designed the bridge had a previous collapse during another bridge construction effort.

•Because of the West Gate Bridge collapse, the bridge designers were forced to redesign the bridge.

Overhead 7

Causes of the West Gate Bridge Collapse

•The main cause of the bridge collapse was the removal of bolts in order to join sections of the bridge together.

•Portions of the bridge were preassembled on the ground.

•As one of the sections was being lifted, some bridge members buckled. It was thought that the buckled section could be repaired when in place.

•As the next section was brought into place, the sections could not be connected due to buckling in the previous section.

•Various methods were used to try to bring the sections into alignment, but buckling of the entire structure occurred.

•Temporary support structures were used during construction, as well as hydraulic jacks.

•Engineers in charge of this project assumed a symmetric structure, instead of asymmetric, as the bridge was constructed. This assumption made the calculations incorrect, and consequently contributed to the buckling.

•The circumstances of this collapse were very complex, but ultimately the designer's mistakes led to buckling.

 

Overhead 8

Conclusion

•Engineers are ultimately responsible for their designs and the resulting consequences.

•Loading requirements and evolving material properties throughout the life-cycle of the system are important elements to be considered in design.

•Buckling is a very important failure mode to consider for applications where the structure is not as stable during construction as it is in its finished form.

Buckling Lecture Handout

1. Designing for Assembly
1. Engineers are responsible for their designs in all stages of product life, including during construction, continuing through the life of the structure, and disposal once the system becomes obsolete.
2. Engineers must be aware of loading requirements and evolving material properties when designing and account for the life cycle requirements.
3. Buckling is an issue that must be dealt with in the design phase.
1. Even though a structure is designed to be stable in the final form, it must also be resistant to buckling while in transit and under construction.
2. Buckling is mostly a function of the length-to-width ratio for members under axial compressive loading. Under such conditions, pure compression failure is rare in materials like concrete or steel.
3. As discussed in class, cross-sectional area, excessive unsupported length, and the modulus of elasticity of the material also play important roles. Yield strength is not an issue in pure buckling.
4. An example of buckling while a structure is under construction may occur when bridges are being fabricated.
5. When a bridge is under construction, some members might be in compression that were designed to withstand tensile forces during service. Unless this condition is considered during design, members may buckle, causing the structure to fail during construction.
6. During bridge construction, many factors must be considered, including
1. bridge span weight distribution,
2. wind forces,
3. temperature effects,
4. and other stresses, some acting in combination.
7. Due to the many unknowns, higher safety factors may be needed to reduce the chance of buckling.
2. West Gate Bridge
1. The West Gate Bridge, built in Melbourne, Australia, collapsed during construction in October 1970.
1. At the time, the British safety factor for bridges was 1.70 (Ross, 177), based on usage allowable loading. However, for construction, the safety factor was only 1.31.

1. The full length bridge was to be five spans of cable-stayed steel box girders, with support given by prestressed concrete approach viaducts. The bridge was 8500 feet in length.
1. Underneath the section of the bridge that collapsed were site huts. Approximately 35 people were killed and many others were injured.
2. The engineers who designed the bridge had a previous collapse during another bridge construction effort.
3. Because of the West Gate Bridge collapse, the bridge designers were forced to redesign the bridge.
1. Causes of the West Gate Bridge Collapse
1. The main cause of the bridge collapse was the removal of bolts in order to join sections of the bridge together.
2. Portions of the bridge were preassembled on the ground.
3. As one of the sections was being lifted, some bridge members buckled. It was thought that the buckled section could be repaired when in place.
4. As the next section was brought into place, the sections could not be connected due to buckling in the previous section.
5. Various methods were used to try to bring the sections into alignment, but buckling of the entire structure occurred.
6. Temporary support structures were used during construction, as well as hydraulic jacks.
7. Engineers in charge of this project assumed a symmetric structure, instead of asymmetric, as the bridge was constructed. This assumption made the calculations incorrect, and consequently contributed to the buckling.
8. The circumstances of this collapse were very complex, but ultimately the designer's mistakes led to buckling.
1. Conclusion
1. Engineers are ultimately responsible for their designs and the resulting consequences.
2. Loading requirements and evolving material properties throughout the life-cycle of the system are important elements to be considered in design.
3. Buckling is a very important failure mode to consider for applications where the structure is not as stable during construction as it is in its finished form.

Blockley, D.I. The Nature of Structural Design and Safety. Chichester: Ellis Horwood Limited, 1980.

Hibbeler, R.C. Structural Analysis. 3^rd ed. Upper Saddle River, New Jersey: Prentice Hall, Inc., 1997.

Kaminetzky, Dov. Design and Construction Failures: Lessons From Forensic Investigations. New York: McGraw-Hill, Inc., 1991.

Ross, Steven S. Construction Disasters: Design Failures, Causes, and Prevention. New York: McGraw-Hill, Inc., 1984.

Buckling Assignment

1. Design the Howe truss bridge in Figure 1 so that it can withstand the indicated loading. Assume

that each truss member is to have a solid, cylindrical cross section of minimum diameter. Also,

each member is to be constructed of structural steel with a yield strength of 36 ksi and a modulus of

elasticity of 29 x 10³ ksi. Ignore the factor of safety. Show your work.

L_AH=L_HG=L_GF=L_FE=50 feet

L_AB = 100feet

Figure 1: Loading of Completed Bridge

 

Sample Calculations (note that there are additional requirements included below):

By inspection ("zero-force" member rules), F_CG = 10 kip (T).

Also, you should find that F_AB = 17.32 kip (C).

For yielding of a straight member under axial loading:

For member AB:

For member CG:

Solving for d:

This also converts member lengths to inches.

For member AB:

For member CG: It is in tension in the bridge's final configuration so buckling would not be an issue.

Member	Length (ft)	Force (kip)	d (yielding, in)	d (buckling, in)	d (design, in)
AB	100	17.32 (C)	0.783	6.49	6.49
CG	86.6	10.00 (T)	0.595	tension	0.595

2. During construction, the bridge will be lifted in the center by a crane and held on the sides by

guy wires. The loading will be as shown in Figure 2. Would the member sizes computed in

problem #1 be safe? If not, why? Show all work. Assume that the 5 kip forces act along the

same lines as members AB and DE.

Figure 2: Bridge Loading During Construction

3. Is a cylindrical cross section an efficient cross section? Explain your answer with an example.

4. What is the lesson to be learned from these problems?