Final answer:
To find the maximum normal stress in a cantilever beam, calculate the weight of the load and the beam, then use the force and cross-sectional area to apply Equation 12.34. For temperature-related stress, use the material's Young's modulus and the coefficient of thermal expansion. Stress varies along the beam's length, with the the largest at the point of greatest weight.
Step-by-step explanation:
To determine the maximum normal stress in a cantilever beam, we begin by calculating the weight of any loads applied to the beam. If we're considering a column or pillar, we'd also include its own weight. The normal force at any point along the beam is the total weight it supports at that point. Once the normal force is known, we apply Equation 12.34, which relates stress to force and cross-sectional area. If needed, the compressive strain can be found using the material's Young's modulus and inverting Equation 12.36.
For temperature-induced stress, as in a steel beam with temperature change from -15 °C to 40 °C with constrained expansion, we use the steel's Young's modulus and the coefficient of thermal expansion to calculate this stress. The stress can also vary along the length of the beam; it is generally the largest where the most weight is applied and decreases along the length away from that point. This is important when calculating the stress distribution in objects like rods or wires under their own weight, where the stress is not uniform.