question archive The solid, concrete cylinder shown below has a radius of 4 in and is subjected to equal magnitude, but opposite sign external point torques T = 200 ft - lb and axial compressive forces of P = 2500 lb at both ends too
The solid, concrete cylinder shown below has a radius of 4 in and is subjected to equal magnitude, but opposite sign external point torques T = 200 ft - lb and axial compressive forces of P = 2500 lb at both ends too
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The solid, concrete cylinder shown below has a radius of 4 in and is subjected to equal magnitude, but opposite sign external point torques T = 200 ft - lb and axial compressive forces of P = 2500 lb at both ends too. The concrete used to make the cylinder has a compression strength of f; = 5000 psi. However, the concrete is much weaker in tension. The tensile strength, 3'}, or modulus of rupture, as it is often called in concrete design manuals and textbooks, is related to the compression strength according to f, = 7.5m. Both the input f]; and output f, are assumed to be in units of psi, when using this equation. P (a) Assuming a state of plane stress, what is the larger, in-plane principal stress, 0'1 (in ksi), on the outer surface of the concrete cylinder? (b) Assuming a state of plane stress, What is the smaller, in-plane principal stress, 0'2 (in ksi), on the outer surface of the concrete cylinder? (c) Using Rankine's Maximum Normal Stress failure theory for brittle materials, de- termine if the cylinder will fail due to the applied loads. (d) What is the factor of safety, FS' = max{asmngth/aappued), against failure? (e) By-hand Submission Only: Sketch the failure envelope in principal stress space {i.e. on a 01-02 axes graph) and plot the point corresponding to the state of stress determined in parts (b) and (c).
