Sir, could you explain why the deformation due to load & temperature of brass & copper are subtracted instead of being added?

Link: /reviewer/mechanics-and-strength-of-materials/solution-to-problem-275-thermal-stress#comment-7829

Engineering Mathematics

February 28, 2015 - 6:11pm

#1
Re: Solution to Problem 275 Thermal Stress

Sir, could you explain why the deformation due to load & temperature of brass & copper are subtracted instead of being added?

Link: /reviewer/mechanics-and-strength-of-materials/solution-to-problem-275-thermal-stress#comment-7829

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Initially, both the copper and brass do not have deformation as indicated by the problem to be stress-free. A drop in temperature will cause the rods to shorten (negative deformation). Both rods will pull the bar against each other causing a tensile stress (positive deformation) in each rod.

sir i just have something in mind,,,

given this problem,,,

A rigid horizontal bar of negligible mass is connected to two rods as shown in Fig. P-275. If the system is initially stress-free.

Calculate the temperature change that will cause a tensile stress of 90 MPa in the brass rod.Assume that both rods are subjected to the change in temperature.,, sir from the bold italic sentence,,, isn't it that the stress due to the change in temp is 95Mpa? and not the total tensile stress due to the load and the change in temperature? heheheh so can't I just have this formula,, [(PL)/(AE)]=[deltaTxLxalphacoefficient] ,,, just asking sir sorry if i may have caused you a problem hehehe,,, things like such makes my mind ZZZzzz uneasy,,, but still i will refer to the solution given ,,, it is sort correct however I only have that question from a part of my brain that tells me,,, thank you,,,

to my fellow students: i don't have an intention of making things go wrong ,,, please refer to the answers given,,, I am still a student that has many questions with such things,,, also has lot of things to learn. refer to experts please,,,thank you

Think back the basic of thermal stress. Assume first that the rods are detached from the bar when ΔT occurs. Being free to expand, there will be no stress in each rod. The rods however are attached to the bar restraining the thermal deformation to the rods. These restrained movements will induced stress (called thermal stress) into the rods which is equivalent to P / A.

From how the rods are attached to the bar, their thermal deformation are influenced by each other. We use the geometry of their movement to create our equation for δ which is a function of thermal stress.