**Overview:**

This 1910 paper, “Expansion of Pipes”, by Ralph C. Taggart, addresses the crucial issue of accommodating pipe expansion in steam piping systems. The author highlights the significant stress that temperature variations can induce in pipes, particularly in high-pressure steam applications. Taggart details the limitations of relying solely on the elasticity of the metal to absorb expansion, emphasizing the need for engineered solutions. He delves into two primary methods: expansion joints and pipe bending.

Taggart critiques various expansion joint designs, noting their drawbacks in terms of leakage, maintenance, and limitations in expansion capacity. He argues that pipe bending, while often based on experience rather than precise calculation, is a more reliable and practical approach. To facilitate accurate calculations, he presents a series of diagrams and curves that allow engineers to determine the necessary length of pipe required to accommodate specific expansion amounts, taking into account both primary and secondary expansions. The paper further explores the benefits of “cold strain” – intentionally introducing a strain in the opposite direction of expansion when the pipe is cold – to mitigate expansion stresses. The author showcases a real-world example where cold strain was successfully used to remedy a leaking steam pipe.

**Key Findings:**

**Expansion stress can exceed safe working limits in steam piping.**The paper emphasizes that the elasticity of the metal alone is often insufficient to handle expansion in high-pressure applications.**Expansion joints are not always the ideal solution.**Taggart outlines several drawbacks of various expansion joint types, including potential leakage, maintenance demands, and limitations in their expansion capacity.**Pipe bending offers a more practical and reliable approach to managing expansion.**While often based on experience, Taggart provides a framework for precise calculations to determine the required lengths of pipe to accommodate specific expansions.**Cold strain is a valuable technique for reducing expansion effects.**By intentionally straining the pipe in the opposite direction when cold, engineers can significantly mitigate expansion stress.

**Learning:**

**1. The Importance of Accounting for Expansion in Steam Piping:**

**Details:**This paper highlights the significant strain that temperature variations can place on steam piping. Without proper considerations, these stresses can exceed safe working limits, leading to pipe damage and potential safety hazards.**Key Takeaways:**Engineers must carefully consider the expansion potential of steam piping and employ suitable solutions, such as expansion joints or pipe bending, to accommodate these changes.

**2. Understanding Expansion Joint Limitations:**

**Details:**Taggart examines several types of expansion joints and outlines their respective limitations, including leakage, maintenance requirements, and restricted expansion capacity.**Key Takeaways:**Expansion joints should be carefully selected based on the specific application and expansion requirements. They are not always the most effective or practical solution, particularly for high-pressure systems.

**3. Utilizing Pipe Bending for Expansion Control:**

**Details:**The paper advocates for pipe bending as a practical method to manage expansion. Taggart provides a framework for precise calculations to determine the necessary pipe lengths to accommodate specific expansion amounts.**Key Takeaways:**By incorporating carefully calculated bends into the piping design, engineers can effectively control expansion without the need for complex expansion joints.

**4. Cold Strain as a Powerful Expansion Mitigation Tool:**

**Details:**Taggart highlights the benefits of “cold strain” – intentionally introducing a strain in the opposite direction of expansion when the pipe is cold. He demonstrates how this technique can significantly reduce expansion stresses and improve piping reliability.**Key Takeaways:**Cold strain is a valuable technique that can be incorporated into piping design to minimize expansion stresses and improve overall system performance.

**Historical Context:**

This paper was written in 1910, a period of rapid industrialization marked by advancements in steam power technology. The growing use of high-pressure steam for power generation and industrial processes led to a demand for more robust and reliable steam piping systems. This context highlights the importance of Taggart’s work in providing a theoretical framework and practical tools for engineers to design piping that could withstand the challenges of high-temperature operation.

**Facts:**

**The modulus of elasticity for wrought iron or steel is 29,000,000.**This is a fundamental property of the material that determines how much it will deform under stress.**The coefficient of expansion for wrought iron 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 this amount.**The stress per degree Fahrenheit difference in temperature for wrought iron is 195.2 lb. per sq. in.**This is calculated by multiplying the modulus of elasticity by the coefficient of expansion.**For a change in temperature of 100 degrees Fahrenheit, the stress in a wrought iron pipe would be 19,520 lb. per sq. in.**This exceeds typical safe working stress limits.**Typical temperature changes in steam apparatus are at least 150 degrees Fahrenheit.**This means that expansion stresses are often significant and require careful management.**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.**The maximum fiber stress in a pipe varies directly with the diameter of the pipe.**Larger diameter pipes will experience higher stresses under the same expansion conditions.**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.**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.**The expansion of a pipe varies directly with the square of its length.**Longer pipes will expand more than shorter pipes under the same temperature change.**The secondary expansion (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.**The three-moment equation is used to calculate the bending moment in a continuous beam.**This equation is derived from fundamental principles of mechanics.**The shear just at the right of the support of a beam can be calculated from the bending moment and load.**This shear force is important for determining the overall stability of the beam.**The bending moment in a pipe under expansion is a maximum at the point where it is held in line.**This means that the pipe is most likely to fail at this point.**The maximum strain in a pipe under expansion is generally less than 1.5 times the strain at the elbow.**This is because the pipe is weaker at the elbow due to the threading and the fitting.**Cold strain is a method of reducing the necessary allowance for expansion by intentionally straining the pipe in the opposite direction when cold.**This reduces the overall expansion stress on the pipe.**A cold strain of 50% of the normal expansion will reduce the strain in the pipe to half the normal strain of expansion.**This can significantly improve the performance and lifespan of the piping system.**A cold strain equal to the expansion will eliminate the strain in the pipe when it is hot.**This means that the pipe will be free of expansion stresses under operating conditions.**The use of standard-weight pipe for bends or expansion loops can reduce the strain on the rest of the piping.**This is because the lighter pipe is more flexible and can accommodate more bending.**The primary or principal expansion is usually the expansion that occurs in the direction of the main pipe run.**This expansion is often the most significant and requires the most careful consideration.

**Statistics:**

**29,000,000:**The modulus of elasticity for wrought iron or steel, indicating its stiffness.**0.00000673:**The coefficient of expansion for wrought iron, showing its expansion per degree Fahrenheit.**195.2:**The stress per degree Fahrenheit in wrought iron pipe, a measure of the force it can withstand.**19,520:**The stress in a wrought iron pipe for a 100 degree Fahrenheit temperature change, highlighting the significant stress that can occur.**150:**The minimum temperature change in typical steam apparatus, emphasizing the need for expansion considerations.**12,000:**The maximum fiber stress used in the paper’s calculations, providing a factor of safety.**16,000:**An alternative maximum fiber stress that can be used with adjusted expansion values in the diagrams.**1.225:**The factor by which lengths should be increased to account for weakening at the elbow, illustrating the importance of considering fitting strength.**1.085:**The factor by which lengths should be increased when considering a secondary expansion, demonstrating the impact of multi-directional expansion.**0.85:**The factor by which expansion should be decreased when accounting for a secondary expansion, illustrating the trade-off between expansion and pipe length.**1/3:**The assumed loss in strength at the elbow, emphasizing the importance of accounting for fitting strength.**2/3:**The reduced strain allowable in a pipe when considering the weakening at the elbow, illustrating the need for safety factors.**1/2:**The reduction in bending potential for an 8-inch pipe compared to a 4-inch pipe with the same length, showing the impact of pipe diameter.**21.2:**The equivalent length of 4-inch pipe for 30 feet of 8-inch pipe, illustrating how to calculate equivalent lengths for different pipe sizes.**20:**The equivalent length of 4-inch pipe for 25 feet of 6-inch pipe, further demonstrating the equivalence calculation.**14.54:**The equivalent length of 4-inch pipe for a combination of 30 feet of 8-inch pipe and 25 feet of 6-inch pipe, demonstrating how to combine equivalent lengths.**179,776:**The combined stiffness of the 6-inch and 8-inch pipes, illustrating how to calculate combined stiffness.**849.44:**The combined stiffness of the 6-inch and 8-inch pipes expressed as a factor of the stiffness of a 4-inch pipe, facilitating comparisons.**211.64:**The equivalent length of 4-inch pipe for the combined stiffness of the 6-inch and 8-inch pipes, demonstrating how to determine the overall length.**35.24:**The combined length of the 4-inch pipe section and the equivalent length of the 6-inch and 8-inch pipe sections, demonstrating the final calculation for the total length.

**Terms:**

**Modulus of Elasticity:**A material property that describes its stiffness or resistance to deformation under stress.**Coefficient of Expansion:**A material property that describes its change in size per degree of temperature change.**Fiber Stress:**The internal stress within a material caused by external forces.**Expansion Joint:**A device designed to accommodate pipe expansion and contraction due to temperature changes, often used in piping systems.**Cold Strain:**The intentional introduction of a strain in the opposite direction of expansion when the pipe is cold, used to mitigate expansion stresses.**Three-Moment Equation:**A mathematical equation used to calculate the bending moment in a continuous beam, an essential tool for structural analysis.**Bending Moment:**The internal moment in a beam caused by external forces, a crucial factor in determining beam strength and stability.**Shear Force:**The internal force that acts perpendicular to the cross-section of a beam, another important factor in determining its strength and stability.**Equivalent Length:**The length of a pipe with a different diameter that would have the same bending resistance as another pipe section.**Stiffness:**A measure of a material’s resistance to deformation under stress.

**Examples:**

**Example of Expansion Stress Exceeding Safe Limits:**The paper states that for a 100-degree Fahrenheit temperature change, the stress in a wrought iron pipe would reach 19,520 lb. per sq. in., exceeding typical safe working stress limits. This illustrates the significant strain that can occur in steam piping and the need for engineered solutions.**Example of Expansion Joint Limitations:**Taggart discusses a type of expansion joint with a sliding metal cylinder, noting 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 highlights the importance of proper design and installation for expansion joints.**Example of Using Pipe Bending for Expansion Control:**Taggart’s paper includes diagrams that illustrate how to calculate the required length of a pipe section to accommodate specific expansion amounts. These diagrams can be used to design piping systems that incorporate calculated bends to effectively manage expansion without the need for expansion joints.**Example of Cold Strain to Remedy a Leaking Steam 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.**Example of Calculating Equivalent Lengths for Different Pipe Sizes:**The paper illustrates how to calculate the equivalent length of a 4-inch pipe for a section of 8-inch pipe, taking into account the difference in bending resistance. This shows how to account for pipe diameter variations in expansion calculations.**Example of Combining Equivalent Lengths for Multiple Pipe Sections:**The paper demonstrates how to combine the equivalent lengths of multiple pipe sections with different diameters to determine the overall equivalent length. This process is crucial for accurately calculating expansion in complex piping systems.**Example of Using Cold Strain to Reduce Expansion Stress:**The paper describes how introducing a cold strain equal to the expansion will completely eliminate expansion stress when the pipe is hot. This illustrates the potential for cold strain to significantly improve piping performance and reliability.**Example of Using Lighter Pipe for Bends to Reduce Strain:**The paper discusses the use of standard-weight pipe for bends or expansion loops while using extra heavy pipe for the rest of the piping. This approach reduces strain on the rest of the piping by allowing for greater flexibility in the bend.**Example of Determining the Principal Expansion:**The paper highlights that the principal expansion is usually the expansion that occurs in the direction of the main pipe run. This understanding is crucial for accurately determining the most significant expansion and designing appropriate solutions.**Example of Using the Diagrams for Different Maximum Fiber Stresses:**The paper notes that the diagrams can be used with higher maximum fiber stresses by proportionally adjusting the expansion values. This demonstrates the flexibility and adaptability of the presented calculations.

**Conclusion:**

This 1910 paper, “Expansion of Pipes,” by Ralph C. Taggart, serves as a valuable resource for engineers designing steam piping systems. It underscores the importance of accounting for pipe expansion due to temperature variations, particularly in high-pressure applications. While expansion joints can play a role, Taggart argues that pipe bending is a more practical and reliable solution. He provides a framework for calculating the required lengths of pipe to accommodate specific expansions, taking into account both primary and secondary expansions. The paper also highlights the advantages of cold straining – intentionally introducing a strain in the opposite direction of expansion when the pipe is cold – to minimize expansion stresses. Taggart’s insights and practical tools continue to be relevant for modern piping design, ensuring that steam piping systems can operate safely and efficiently under a wide range of temperature conditions.