**What is the modulus of elasticity for wrought iron or steel?**

- 29,000,000
- 19,520
- 150
- 0.00000673

Correct Answer: 29,000,000

Correct Answer Explanation: The modulus of elasticity is a fundamental property of a material that describes its stiffness or resistance to deformation under stress. For wrought iron or steel, the modulus of elasticity is 29,000,000. This means that the material will resist deformation with a force of 29,000,000 pounds per square inch.

**What is the coefficient of expansion for wrought iron?**

- 29,000,000
- 19,520
- 150
- 0.00000673

Correct Answer: 0.00000673

Correct Answer Explanation: The coefficient of expansion is a material property that describes how much it will expand or contract per degree of temperature change. For wrought iron, the coefficient of expansion is 0.00000673 per degree Fahrenheit. This means that for every degree Fahrenheit increase in temperature, a unit length of wrought iron will expand by 0.00000673 units.

**Which type of expansion joint was described as potentially having issues if not properly anchored?**

- Expansion joints with a sliding metal cylinder
- Expansion joints with a bellows design
- Expansion joints with a flexible rubber gasket
- Expansion joints with a hinged pipe section

Correct Answer: Expansion joints with a sliding metal cylinder

Correct Answer Explanation: The paper discussed the limitations of expansion joints, including those with a sliding metal cylinder. The author noted that if the joint is not properly anchored, the movement of the pipe can carry the inner cylinder entirely away from the outer cylinder, leading to failure. This illustrates the importance of proper design and installation for expansion joints.

**How does cold strain help reduce expansion stresses in a pipe?**

- Cold strain makes the pipe more elastic
- Cold strain reduces the pipe’s coefficient of expansion
- Cold strain introduces a strain in the opposite direction of expansion when the pipe is cold, reducing expansion stress.
- Cold strain makes the pipe more resistant to bending

Correct Answer: Cold strain introduces a strain in the opposite direction of expansion when the pipe is cold, reducing expansion stress.

Correct Answer Explanation: Cold strain is a valuable technique that engineers can use to mitigate expansion stresses. It involves intentionally straining the pipe in the opposite direction of expansion when the pipe is cold. This pre-strain helps to offset the expansion that will occur when the pipe heats up, reducing the overall stress on the pipe. The paper describes a case where a leaking steam pipe in a hotel was successfully repaired by using a shorter replacement pipe section, intentionally introducing a cold strain to counteract the expansion stress. This demonstrates the practical application of cold strain in mitigating expansion problems.

**What is the term for the expansion that occurs in the direction of the main pipe run?**

- Secondary expansion
- Principal expansion
- Tertiary expansion
- Lateral expansion

Correct Answer: Principal expansion

Correct Answer Explanation: The principal expansion is the expansion that occurs in the direction of the main pipe run. It is often the most significant expansion and requires the most careful consideration in designing piping systems. Understanding the principal expansion is crucial for determining the most effective methods to accommodate expansion and prevent excessive stress on the piping.

**What is the term for the length of a pipe with a different diameter that would have the same bending resistance as another pipe section?**

- Equivalent length
- Effective length
- Actual length
- Nominal length

Correct Answer: Equivalent length

Correct Answer Explanation: The concept of equivalent length is important for accurately calculating expansion in piping systems with multiple pipe sections of different diameters. It allows engineers to determine the length of a pipe with a standard diameter that would have the same bending resistance as a section of pipe with a different diameter. By using equivalent lengths, engineers can simplify calculations and ensure that the overall piping system is designed to effectively manage expansion.

**What is the term for the internal force that acts perpendicular to the cross-section of a beam?**

- Shear force
- Bending moment
- Tensile force
- Compressive force

Correct Answer: Shear force

Correct Answer Explanation: Shear force is a critical factor in determining the strength and stability of a beam or pipe. It is the internal force that acts perpendicular to the cross-section of the beam. Understanding shear forces is essential for engineers designing piping systems to ensure that they can withstand the stresses caused by expansion and contraction.

**What is the term for the internal moment in a beam caused by external forces?**

- Shear force
- Bending moment
- Tensile force
- Compressive force

Correct Answer: Bending moment

Correct Answer Explanation: The bending moment is another crucial factor in determining the strength and stability of a beam or pipe. It is the internal moment caused by external forces acting on the beam, which creates stresses within the material. Understanding bending moments is essential for engineers designing piping systems to ensure that they can withstand the stresses caused by expansion and contraction.

**Why is the bending moment in a pipe under expansion a maximum at the point where it is held in line?**

- This is where the pipe is weakest
- This is where the pipe is most likely to fail
- This is where the pipe experiences the most stress
- All of the above

Correct Answer: All of the above

Correct Answer Explanation: The bending moment in a pipe under expansion is a maximum at the point where it is held in line because this is where the pipe is most likely to fail. The stress on the pipe is highest at this point, making it the weakest point in the system. This is why it’s critical for engineers to carefully consider the bending moment in their designs and ensure that the pipe is adequately supported to handle the stresses caused by expansion.

**What is the term for the intentional introduction of a strain in the opposite direction of expansion when the pipe is cold?**

- Cold strain
- Expansion compensation
- Stress relief
- Pre-bending

Correct Answer: Cold strain

Correct Answer Explanation: Cold strain is a valuable technique for mitigating expansion stresses in piping systems. It involves intentionally straining the pipe in the opposite direction of expansion when the pipe is cold. This pre-strain helps to offset the expansion that will occur when the pipe heats up, reducing the overall stress on the pipe. The paper describes a case where a leaking steam pipe in a hotel was successfully repaired by using a shorter replacement pipe section, intentionally introducing a cold strain to counteract the expansion stress. This demonstrates the practical application of cold strain in mitigating expansion problems.

**How does cold strain reduce the strain in a pipe when it is hot?**

- It increases the pipe’s modulus of elasticity
- It decreases the pipe’s coefficient of expansion
- It offsets the expansion that occurs when the pipe heats up
- It makes the pipe more resistant to bending

Correct Answer: It offsets the expansion that occurs when the pipe heats up

Correct Answer Explanation: Cold strain works by introducing a strain in the opposite direction of expansion when the pipe is cold. This pre-strain helps to offset the expansion that will occur when the pipe heats up, reducing the overall stress on the pipe. For example, if a pipe is expected to expand by 1 inch when hot, a cold strain of 0.5 inches would reduce the actual expansion to 0.5 inches. This significantly reduces the stress on the pipe, improving its performance and lifespan.

**How much of a cold strain is needed to eliminate the strain in a pipe when it is hot?**

- 50% of the normal expansion
- Equal to the expansion
- 100% of the normal expansion
- Double the normal expansion

Correct Answer: Equal to the expansion

Correct Answer Explanation: If a cold strain equal to the expansion is introduced, it will completely eliminate the strain in the pipe when it is hot. This is because the pre-strain will perfectly offset the expansion that occurs when the pipe heats up. This is a very effective way to minimize expansion stress and ensure the long-term reliability of the piping system.

**What is the benefit of using standard-weight pipe for bends or expansion loops while using extra heavy pipe for the rest of the piping?**

- It reduces the overall weight of the piping system
- It allows for greater flexibility in the bends
- It increases the strength of the piping system
- It reduces the cost of the piping system

Correct Answer: It allows for greater flexibility in the bends

Correct Answer Explanation: Using standard-weight pipe for bends or expansion loops while using extra heavy pipe for the rest of the piping is a common practice in piping design. This approach is beneficial because it allows for greater flexibility in the bends, which helps to accommodate expansion and contraction without putting excessive stress on the rest of the piping. The lighter pipe can bend more easily, reducing the strain on the heavier, more rigid sections.

**What is the maximum fiber stress used in the paper’s calculations?**

- 19,520 lb per sq in
- 12,000 lb per sq in
- 16,000 lb per sq in
- 29,000,000 lb per sq in

Correct Answer: 12,000 lb per sq in

Correct Answer Explanation: The paper’s author used a maximum fiber stress of 12,000 lb per sq in in his calculations. This was a commonly accepted value at the time and provided a margin of safety for the pipes. It’s important to note that this value could be adjusted based on the specific application and the desired level of safety.

**What is the minimum temperature change that the paper states is typical in steam apparatus?**

- 100 degrees Fahrenheit
- 150 degrees Fahrenheit
- 200 degrees Fahrenheit
- 250 degrees Fahrenheit

Correct Answer: 150 degrees Fahrenheit

Correct Answer Explanation: The paper states that typical temperature changes in steam apparatus are at least 150 degrees Fahrenheit. This means that expansion stresses are often significant and require careful management to prevent damage to the pipes. Engineers designing steam piping systems must take these temperature changes into account and use appropriate methods to accommodate expansion and contraction.

**How does the maximum fiber stress in a pipe vary with the amount of expansion?**

- It varies directly with the amount of expansion.
- It varies inversely with the amount of expansion.
- It is not affected by the amount of expansion.
- It varies proportionally to the square of the amount of expansion.

Correct Answer: It varies directly with the amount of expansion.

Correct Answer Explanation: The maximum fiber stress in a pipe varies directly with the amount of expansion. This means that if the expansion doubles, the stress will also double. This relationship is important to consider when designing piping systems, as it highlights the importance of minimizing expansion to reduce stress on the pipe.

**How does the maximum fiber stress in a pipe vary with the diameter of the pipe?**

- It varies directly with the diameter of the pipe.
- It varies inversely with the diameter of the pipe.
- It is not affected by the diameter of the pipe.
- It varies proportionally to the square of the diameter of the pipe.

Correct Answer: It varies directly with the diameter of the pipe.

Correct Answer Explanation: The maximum fiber stress in a pipe varies directly with the diameter of the pipe. This means that larger diameter pipes will experience higher stresses under the same expansion conditions. This is because larger diameter pipes have a larger surface area that is subject to the same amount of expansion, resulting in higher overall stress.

**How does the expansion of a pipe vary with its outside diameter?**

- It varies directly with the outside diameter.
- It varies inversely with the outside diameter.
- It is not affected by the outside diameter.
- It varies proportionally to the square of the outside diameter.

Correct Answer: It varies inversely with the outside diameter.

Correct Answer Explanation: The expansion of a pipe varies inversely with its outside diameter. This means that a larger diameter pipe will expand less than a smaller diameter pipe under the same temperature change. This is because the larger diameter pipe has a larger cross-sectional area, which distributes the expansion stress more evenly.

**How does the maximum fiber stress in a pipe vary with its length?**

- It varies directly with the length of the pipe.
- It varies inversely with the length of the pipe.
- It is not affected by the length of the pipe.
- It varies proportionally to the square of the length of the pipe.

Correct Answer: It varies inversely with the square of its length.

Correct Answer Explanation: The maximum fiber stress in a pipe varies inversely with the square of its length. This means that longer pipes will experience lower stresses under the same expansion conditions. This is because the expansion is distributed over a larger length, reducing the stress at any given point.

**How does the expansion of a pipe vary with its length?**

- It varies directly with the length of the pipe.
- It varies inversely with the length of the pipe.
- It is not affected by the length of the pipe.
- It varies proportionally to the square of the length of the pipe.

Correct Answer: It varies directly with the square of its length.

Correct Answer Explanation: The expansion of a pipe varies directly with the square of its length. This means that longer pipes will expand more than shorter pipes under the same temperature change. This relationship is important for engineers to consider when designing piping systems, as it highlights the need to carefully manage the length of pipes to minimize expansion and reduce stress on the system.

**How does the secondary expansion of a pipe (at right angles to the principal expansion) compare to the principal expansion?**

- It is usually greater than two times the principal expansion.
- It is usually less than two times the principal expansion.
- It is equal to the principal expansion.
- It is unpredictable and can vary widely.

Correct Answer: It is usually less than two times the principal expansion.

Correct Answer Explanation: The secondary expansion of a pipe, which occurs at right angles to the principal expansion, is usually less than two times the principal expansion. This is because the pipe is more resistant to bending in the direction of the principal expansion. Understanding the relationship between primary and secondary expansions is important for engineers designing piping systems to accurately account for the overall expansion and ensure that the system can handle the stresses.

**What is the three-moment equation used to calculate?**

- The shear force in a continuous beam
- The bending moment in a continuous beam
- The deflection of a continuous beam
- The stress in a continuous beam

Correct Answer: The bending moment in a continuous beam

Correct Answer Explanation: The three-moment equation is a mathematical equation used to calculate the bending moment in a continuous beam. This equation is derived from fundamental principles of mechanics and is a powerful tool for engineers analyzing and designing structures. The bending moment is an essential factor in determining the strength and stability of a beam.

**How can the shear just at the right of the support of a beam be calculated?**

- From the bending moment and the load
- From the load and the deflection
- From the deflection and the stress
- From the stress and the modulus of elasticity

Correct Answer: From the bending moment and the load

Correct Answer Explanation: The shear just at the right of the support of a beam can be calculated from the bending moment and the load. This shear force is important for determining the overall stability of the beam. Understanding shear forces is essential for engineers designing piping systems to ensure that they can withstand the stresses caused by expansion and contraction.

**What is the term for the stress within a material caused by external forces?**

- Fiber stress
- Tensile stress
- Compressive stress
- Shear stress

Correct Answer: Fiber stress

Correct Answer Explanation: Fiber stress is the internal stress within a material caused by external forces. This stress is distributed throughout the material and can be measured in pounds per square inch (psi). Understanding fiber stress is essential for engineers designing piping systems to ensure that they can withstand the stresses caused by expansion and contraction.

**What is the factor by which lengths should be increased to account for weakening at the elbow?**

- 1.085
- 1.225
- 0.85
- 1.15

Correct Answer: 1.225

Correct Answer Explanation: The paper notes that the strength of the pipe is reduced at the elbow due to the threading and the fitting. This weakening needs to be accounted for in expansion calculations. The factor 1.225 is used to increase the calculated length of the pipe to compensate for this weakening.

**What is the factor by which lengths should be increased when considering a secondary expansion?**

- 1.085
- 1.225
- 0.85
- 1.15

Correct Answer: 1.085

Correct Answer Explanation: The secondary expansion of a pipe, which occurs at right angles to the principal expansion, needs to be considered when calculating the overall expansion of the piping system. The factor 1.085 is used to increase the calculated length of the pipe to account for this additional expansion.

**What is the factor by which expansion should be decreased when accounting for a secondary expansion?**

- 1.085
- 1.225
- 0.85
- 1.15

Correct Answer: 0.85

Correct Answer Explanation: The paper notes that the secondary expansion is usually less than two times the principal expansion. This is because the pipe is more resistant to bending in the direction of the principal expansion. The factor 0.85 is used to decrease the calculated expansion to account for this reduction in secondary expansion.

**What is the assumed loss in strength at the elbow?**

- 1/2
- 1/3
- 1/4
- 1/5

Correct Answer: 1/3

Correct Answer Explanation: The paper notes that the strength of the pipe is reduced at the elbow due to the threading and the fitting. The paper assumes that the loss in strength at the elbow is 1/3.

**What is the reduced strain allowable in a pipe when considering the weakening at the elbow?**

- 1/2
- 1/3
- 1/4
- 1/5

Correct Answer: 2/3

Correct Answer Explanation: The paper notes that the strain allowable in a pipe needs to be reduced when considering the weakening at the elbow. The paper assumes that the reduced strain allowable is 2/3. This helps ensure that the pipe can withstand the stresses caused by expansion without failing.

**What is the reduction in bending potential for an 8-inch pipe compared to a 4-inch pipe with the same length?**

- 1/2
- 1/3
- 1/4
- 1/5

Correct Answer: 1/2

Correct Answer Explanation: The paper notes that the bending potential of a pipe is inversely proportional to its diameter. This means that an 8-inch pipe will have half the bending potential of a 4-inch pipe with the same length. This is important to consider when designing piping systems, as it highlights the need to carefully manage the diameter of the pipes to ensure that they can handle the stresses caused by expansion and contraction.

**What is the equivalent length of 4-inch pipe for 30 feet of 8-inch pipe?**

- 14.54 feet
- 21.2 feet
- 20 feet
- 30 feet

Correct Answer: 21.2 feet

Correct Answer Explanation: The equivalent length of a pipe is the length of a pipe with a different diameter that would have the same bending resistance. The paper provides a table of equivalent lengths for different pipe sizes. According to the table, 30 feet of 8-inch pipe has an equivalent length of 21.2 feet of 4-inch pipe.

**What is the equivalent length of 4-inch pipe for 25 feet of 6-inch pipe?**

- 14.54 feet
- 21.2 feet
- 20 feet
- 30 feet

Correct Answer: 20 feet

Correct Answer Explanation: The equivalent length of a pipe is the length of a pipe with a different diameter that would have the same bending resistance. The paper provides a table of equivalent lengths for different pipe sizes. According to the table, 25 feet of 6-inch pipe has an equivalent length of 20 feet of 4-inch pipe.

**What is the equivalent length of 4-inch pipe for a combination of 30 feet of 8-inch pipe and 25 feet of 6-inch pipe?**

- 14.54 feet
- 21.2 feet
- 20 feet
- 30 feet

Correct Answer: 14.54 feet

Correct Answer Explanation: The equivalent length of a pipe is the length of a pipe with a different diameter that would have the same bending resistance. The paper provides a table of equivalent lengths for different pipe sizes. According to the table, 30 feet of 8-inch pipe has an equivalent length of 21.2 feet of 4-inch pipe, and 25 feet of 6-inch pipe has an equivalent length of 20 feet of 4-inch pipe. The combined equivalent length is 21.2 + 20 = 41.2 feet. The paper also provides a table for calculating the equivalent length for a combination of different pipe sizes. According to this table, 41.2 feet of 4-inch pipe is equivalent to 14.54 feet of 4-inch pipe.

**What is the combined stiffness of the 6-inch and 8-inch pipes, expressed as a factor of the stiffness of a 4-inch pipe?**

- 179,776
- 849.44
- 211.64
- 35.24

Correct Answer: 849.44

Correct Answer Explanation: The stiffness of a pipe is a measure of its resistance to deformation under stress. The paper provides a table for calculating the combined stiffness of multiple pipe sections. The combined stiffness of the 6-inch and 8-inch pipes is 179,776. The stiffness of a 4-inch pipe is 211.64. The combined stiffness of the 6-inch and 8-inch pipes, expressed as a factor of the stiffness of a 4-inch pipe, is 179,776 / 211.64 = 849.44.

**What is the equivalent length of 4-inch pipe for the combined stiffness of the 6-inch and 8-inch pipes?**

- 179,776
- 849.44
- 211.64
- 35.24

Correct Answer: 211.64

Correct Answer Explanation: The equivalent length of a pipe is the length of a pipe with a different diameter that would have the same bending resistance. The paper provides a table for calculating the equivalent length for different pipe sizes. According to this table, the equivalent length of 4-inch pipe for the combined stiffness of the 6-inch and 8-inch pipes is 211.64 feet.

**What is the combined length of the 4-inch pipe section and the equivalent length of the 6-inch and 8-inch pipe sections?**

- 179,776
- 849.44
- 211.64
- 35.24

Correct Answer: 35.24

Correct Answer Explanation: The combined length of the 4-inch pipe section and the equivalent length of the 6-inch and 8-inch pipe sections is 35.24 feet. This is calculated by adding the length of the 4-inch pipe section to the equivalent length of the 6-inch and 8-inch pipe sections. This is an important step in calculating the overall expansion of a piping system.

**What is the term for a device designed to accommodate pipe expansion and contraction due to temperature changes?**

- Expansion joint
- Cold strain
- Bellows
- None of the above

Correct Answer: Expansion joint

Correct Answer Explanation: An expansion joint is a device designed to accommodate pipe expansion and contraction due to temperature changes. They are often used in piping systems to prevent excessive stress on the pipe and to prevent leaks. Expansion joints come in a variety of designs, each with its own advantages and disadvantages.

**What is the term for a mathematical equation used to calculate the bending moment in a continuous beam?**

- Three-moment equation
- Expansion equation
- Stress equation
- Deflection equation

Correct Answer: Three-moment equation

Correct Answer Explanation: The three-moment equation is a mathematical equation used to calculate the bending moment in a continuous beam. This equation is derived from fundamental principles of mechanics and is a powerful tool for engineers analyzing and designing structures. The bending moment is an essential factor in determining the strength and stability of a beam.

**What is the term for a measure of a material’s resistance to deformation under stress?**

- Modulus of elasticity
- Coefficient of expansion
- Stress
- Strain

Correct Answer: Modulus of elasticity

Correct Answer Explanation: The modulus of elasticity is a material property that describes its stiffness or resistance to deformation under stress. It is a measure of how much force is required to deform a material by a given amount. The higher the modulus of elasticity, the stiffer the material.

**What is the term for a material property that describes its change in size per degree of temperature change?**

- Modulus of elasticity
- Coefficient of expansion
- Stress
- Strain

Correct Answer: Coefficient of expansion

Correct Answer Explanation: The coefficient of expansion is a material property that describes its change in size per degree of temperature change. Different materials have different coefficients of expansion. For example, steel has a higher coefficient of expansion than concrete. This means that steel will expand more than concrete for the same temperature change.

**What is the term for the internal stress within a material caused by external forces?**

- Modulus of elasticity
- Coefficient of expansion
- Stress
- Strain

Correct Answer: Stress

Correct Answer Explanation: Stress is the internal force that acts on a material within a cross-sectional area. It is caused by external forces acting on the material, such as the weight of a structure or the pressure of a fluid. Stress can be measured in pounds per square inch (psi). Understanding stress is essential for engineers designing structures to ensure that they can withstand the loads they are intended to carry.