Thermal Gradient through a Beam

FIGURE 6.2 Example 6.2— Thermal gradient through a beam. 

Vary depth h, thermal conductivity k, elastic modulus E, and coefficient of thermal expansion a to meet the static strength requirement S . 

Compare any two candidate materials, 1 and 2, on a strength basis using the same factor of safety  

From Equation 6.18 the relative depth ratio is established for this problem  

it is found that the size ratio hjh in this case is directly proportional to the strength ratio, whereas in Example 6.1, Equation 6.3, it was inversely proportional to the square root of the strength ratio. Why is this Examine Equations 6.15 and 6.16 O is proportional to AT but AT is proportional to h. However, in the beam bending problem O was inversely proportional to IP in Equation 6.1. The reader should keep in mind this difference in stresses caused by external loads and internal temperature gradients. (As a mental challenge, consider combined external loads with internal temperature gradients.) 

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Prepare a material comparison table for the PF-GP, PF-MI, and PF-high impact (PF-HI) materials for a thermal gradient through a beam on a deflection basis (thermal bowing). 

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