Chapter 4: Problem 75
Is using force flow to study stress in a component an art or a science? Can the concept of force flow be used to study problems where numerical values for loads are indeterminate?
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Chapter 4: Problem 75
Is using force flow to study stress in a component an art or a science? Can the concept of force flow be used to study problems where numerical values for loads are indeterminate?
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A cylinder is internally pressurized to a pressure of \(100 \mathrm{MPa}\). This causes tangential and axial stresses in the outer surface of 400 and \(200 \mathrm{MPa}\), respectively. Make a Mohr circle representation of the stresses in the outer surface. What maximum shear stress is experienced by the outer surface?
Two rectangular beams are made of steel having a tensile yield strength of \(550 \mathrm{MPa}\) and an assumed idealized stress-strain curve. Beam A has a uniform 25 \(\mathrm{mm} \times 12.5-\mathrm{mm}\) section. Beam B has a \(25 \mathrm{~mm} \times 12.5-\mathrm{mm}\) section that blends symmetrically into a \(37.5 \mathrm{~mm} \times 12.5-\mathrm{mm}\) section with fillets giving a stress concentration factor of \(2.5\). The beams are loaded in bending in such a way that \(Z=I / c=b h^{2} / 6=12.5(25)^{2} / 6=1302 \mathrm{~mm}^{3}\). (a) For each beam, what moment, \(M\), causes (1) initial yielding and (2) complete yielding? (b) Beam \(\mathrm{A}\) is loaded to cause yielding to a depth of \(6.35 \mathrm{~mm}\). Determine and plot the distribution of residual stresses that remain after the load is removed.
Limestone blocks approximately 8 in. wide by 14 in. long by 6 in. high are sometimes used in constructing dry stacked walls. If the stability of the wall is not an issue and the only question is the strength of the block in compression, how high could blocks be stacked if the limestone has a compressive strength of \(4000 \mathrm{psi}\) and a density of \(135 \mathrm{lb}\) per cubic foot?
Determine the maximum shear stress at the outer surface of an internally pressurized cylinder where the internal pressure causes tangential and axial stresses in the outer surface of 300 and \(150 \mathrm{MPa}\), respectively.
A uniformly tapered vertical cone with a height, \(h\), and a base diameter, \(d\), is cast from a urethane material having a density, \(\rho\). Determine the compressive stress at the cross section of the base, \(B\), and at the cross section, \(A\), half way up the cone, and compare the compressive stress at \(B\) with the compressive stress at \(A\). The volume of the cone is \(V_{\text {cone }}=(1 / 12) \pi d^{2} h\).
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