Rod deformation with two materials in series

Mark Nussbaum · Dec 10, 2017

Homework Statement

Diagram of a two-segment column in series: upper segment C to B labelled E1 with diameter D1 and length L1, lower segment B to A labelled E2 with diameter D2 and length L2, a load Pc at the top and load PB/2 applied at joint B from each side.

Problem statement text: rod subjected to loads P_B = 137 kN and P_C = 30 kN; segments AB and BC have elastic moduli E_2 = 190 GPa and E_1 = 71 GPa; find overall change in length; assume collar at B is rigid and stress concentrations neglected.

Homework Equations

deformation=(force*length)/(elastic moduli*area)

The Attempt at a Solution

$Sum of two deformation terms written as fractions: first, negative (30000 times 0.22) over 71000000000 times pi times 0.018 squared; second, 137000 times 0.29 over 190000000000 times pi times 0.022 squared, followed by m.$

and

$Sum of two deformation terms written as fractions: first term -(30000 · 0.22) over 71000000000π · 0.018², plus 137000/2 · 0.29 over 190000000000π · 0.022², with unit m.$

since most of the variable are constants it seemed like a simple plug in problem, however it seems that my use of the forces is incorrect. unfortunately we had no examples for this chapter in class and what is in the textbook has not helped me so far. the above is both equations for deformation of each rod summed together top rod first then bottom.

Chestermiller · Dec 10, 2017

From an overall force balance, what is the reaction force at A? What is the tension in AB? What is the tension in BC?

Rod deformation with two materials in series

Homework Statement

Homework Equations

The Attempt at a Solution

Discussion

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