Thermal Stresses in Compound Bars
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Questions and Answers

What is the formula used to relate the compressive stresses in steel and concrete based on their areas and Young's modulus?

  • \( \sigma_s = \frac{W_c A_s E_s}{A_c E_c} \)
  • \( \sigma_c = \frac{W_c A_s E_s}{A_c E_c} \) (correct)
  • \( \sigma_c = \frac{W_s A_c E_c}{A_s E_s} \)
  • \( \sigma_s = \frac{W_s A_c E_c}{A_s E_s} \)

    • Given that Young's modulus for steel is 200 GPa, how is the compressive stress in steel calculated when the total thrust on the column is 1 MN?

  • \( \sigma_s = \frac{1960 \times 200}{248000 + 14} \)
  • \( \sigma_s = \frac{1 \times 10^6 \times 200 \times 10^3}{1960} \)
  • \( \sigma_s = \frac{248000 \times 14 \times 10^3}{1960 + 200 \times 10^3} \)
  • \( \sigma_s = \frac{1960 \times 200 \times 10^3}{248000 + 14 \times 10^3} \) (correct)

    • How does increasing the temperature of a body generally affect its dimensions?

  • It remains unchanged.
  • It expands. (correct)
  • It depends on the material's properties.
  • It contracts.

    • What is the total thrust on the column in Newtons when simplified?

    <p>1 MN</p> Signup and view all the answers

    When calculating the area of concrete around the steel, what dimensions were used?

    <p>500 mm x 500 mm</p> Signup and view all the answers

    What is the approximate compressive stress in concrete when a thrust of 1 MN is applied?

    <p>3.62 MPa</p> Signup and view all the answers

    Which equation represents the equilibrium relationship established for the steel and concrete column?

    <p>( W_c + W_s = 1 MN )</p> Signup and view all the answers

    What does the compatibility equation imply regarding the strains in the steel and concrete?

    <p>Strains in steel and concrete are equal.</p> Signup and view all the answers

    What does the symbol 𝛼 represent in the equation 𝛿𝑇 = 𝐿𝛼 ∆𝑇?

    <p>Expansion coefficient</p> Signup and view all the answers

    Which formula is used to calculate thermal strain from thermal change in length?

    <p>$ rac{𝛿𝑇}{𝐿}$</p> Signup and view all the answers

    What is the relationship between stress and strain as represented in the thermal stress equation?

    <p>$𝜎𝑇 = 𝐸 × 𝜀𝑇$</p> Signup and view all the answers

    If a steel tube encloses a copper rod and the temperature is increased, which material will experience a higher expansion strain given their respective coefficients?

    <p>Copper, as it has a higher expansion coefficient</p> Signup and view all the answers

    What would be the consequence of raising the temperature of a steel tube that encloses a rigidly joined copper rod?

    <p>Both materials will experience tensile stress</p> Signup and view all the answers

    When calculating the stresses in the assembled rod and tube, which modulus of elasticity value is used for steel?

    <p>210,000 MPa</p> Signup and view all the answers

    To find the thermal strain in a member, which parameters must be known?

    <p>Original length, expansion coefficient, and change in temperature</p> Signup and view all the answers

    Given that the expansion coefficients are $𝛼𝑠 = 11 × 10^{-6} /°C$ for steel and $𝛼𝑐 = 18 × 10^{-6} /°C$ for copper, what is the effect of temperature increase on each material?

    <p>Copper will expand more than steel</p> Signup and view all the answers

    What defines a compound bar in mechanics of materials?

    <p>It consists of two or more bars or tubes in parallel, usually of different materials.</p> Signup and view all the answers

    In analyzing a compound bar system, which two conditions must be applied for a proper solution?

    <p>Equilibrium and compatibility conditions.</p> Signup and view all the answers

    What does the variable $W_1$ represent in the equilibrium equation?

    <p>The load taken by the rod.</p> Signup and view all the answers

    If $W_1 + W_2 = P$, what does $P$ represent?

    <p>The external load applied to the compound bar system.</p> Signup and view all the answers

    In the compatibility equation $ rac{W_1}{A_1 E_1} = rac{W_2}{A_2 E_2}$, what does it denote about the strains?

    <p>It indicates that strains are equal for both the rod and tube.</p> Signup and view all the answers

    In a system where $W_1$ and $W_2$ are loads on a compound bar, which of the following equations correctly describes $W_2$?

    <p>$W_2 = rac{W_1 A_2 E_2}{A_1 E_1}$</p> Signup and view all the answers

    Given a concrete column reinforced with steel rods, how does the configuration of the rods affect the overall load-bearing capacity?

    <p>The arrangement of the rods enhances the load capacity of the entire unit.</p> Signup and view all the answers

    What geometric configuration is described for the concrete column reinforced with steel rods?

    <p>Square with rods placed at the corners.</p> Signup and view all the answers

    Study Notes

    Compound Bars

    • A compound bar consists of two or more bars in parallel made of different materials.
    • The main idea of analysis is to apply both equilibrium and compatibility conditions for a solution.
    • Equilibrium Equation: The sum of all forces acting on the bar must equal zero.
    • Compatibility Equation: The strain in each bar must be equal.

    Thermal Stresses

    • Thermal stresses occur when a material is heated or cooled, causing it to expand or contract.
    • Thermal strain is the change in length per unit length caused by a change in temperature.
    • Thermal stress is the stress that exists within a material due to thermal strain.

    Thermal Stress Equation

    • The thermal stress equation is used to calculate the thermal stress in a material.
    • 𝜎𝑇 = 𝜀𝑇 × 𝐸
      • 𝜎𝑇 represents the thermal stress.
      • 𝜀𝑇 represents the thermal strain.
      • 𝐸 represents the modulus of elasticity.

    Example 2

    • A steel tube encloses a copper rod.
    • At 10°C, there is no longitudinal stress.
    • The temperature is raised to 200°C.
    • The goal is to calculate the stresses in the steel rod and copper tube.

    Why Bricks Fall

    • When a brick wall is exposed to high temperatures, the steel rods embedded in the wall expand more than the bricks.
    • This expansion creates tensile stresses within the steel rods, leading to a weakening of the wall.
    • As the temperature continues to increase, the steel rods can eventually fail, leading to the collapse of the wall.

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    Related Documents

    Compound Bars and Thermal Stresses (EGS 21107) 06/10/2024 PDF

    Description

    This quiz covers the concepts of compound bars and thermal stresses, including equilibrium and compatibility conditions. You'll explore the equations that govern thermal stress and strain, focusing on their applications in different materials. Test your understanding of how temperature changes affect structural components.

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