Question 2.10: The shop crane in Fig. 1 consists of a boom AC that is suppo......
The shop crane in Fig. 1 consists of a boom AC that is supported by a pin at A and a rectangular tension bar BD. Details of the pin joints at A and B are shown in Views a − a and b − b, respectively. The tension bar is to be made of structural steel with σ_Y = 36 ksi, while the pins at A and B are to be of high-strength steel with \tau_Y = 48 ksi.
The design (i.e., allowable) load is P = 5 kips, and there is to be a factor of safety with respect to yielding of FS = 3.0. (a) If the width of the bar BD is w = 2 in., determine the required thickness, t, to the nearest 1/8 in. (b) Determine the required pin diameters at A and B to the nearest 1/8 in.
Plan the Solution Equilibrium of boom AC can be used to determine the tension F_B in two-force member BD and the resultant force F_A on the pin at A. Then we can use allowable-stress design (Eq. 2.28) to determine the cross-sectional area of bar BD and the required pin diameters, noting that the pin at A is in double shear and the pin at B is in single shear.
σ_{\text{allow}} = \frac{σ_Y} {FS}, or \tau _{\text{allow}} = \frac{\tau Y} {FS} (2.28)
Equilibrium: Equilibrium equations were used to solve for the forces
F_A and F_B that are shown on the free-body diagram in Fig. 2.
(a) Design of Bar BD: From Eq. 2.28,
σ_{\text{allow}} = \frac{σ_γ}{FS}→σ_{\text{allow}} = \frac{36 ksi}{3.0} = 12 ksi
F_{BD} = σ_{\text{allow}}A_{BD}→A_{BD} = (2 in.)t_{BD} = \frac{10 kips} {12 ksi}t_{BD} = 0.417 in. Select t_{BD} = 0.5 in.
(b) Design of Pins at A and B: From Eq. 2.28,
\tau _{\text{allow}} = \frac{\tau _γ}{FS}→\tau _{\text{allow}} = \frac{48 ksi}{3.0} = 16 ksi
\frac{1}{2}F_A = \tau _{\text{allow}}A_A→A_A = \frac{6.708 kips}{2(16 ksi)} = 0.210 in²
A_A = \frac{\pi d^2_A} {4} → d_A = 0.517 in. Select d_A = 0.625 in.
F_B =\tau _{\text{allow}}A_B → A_B = \frac{10 kips} {16 ksi} = 0.625 in²
A_B = \frac{\pi d^2_B} {4} → d_B = 0.892 in. Select d_B = 1.0 in.
Review the Solution These calculations are very straightforward, but should be double-checked, especially to make sure that the FS has been properly applied. The answers seem to be “reasonable” numbers.
