Question 4.CS.1: Bolt Cutter Deflection Analysis Members 2 and 3 of the bolt ...
Bolt Cutter Deflection Analysis
Members 2 and 3 of the bolt cutter shown in Figure 3.31 are critically stressed. Determine the deflections employing the superposition method.
Given: The dimensions (in inches) and loading are known from Case Study 3.1. The parts are made of AISI 1080 HR steel having E = 30 \times 10^{6} psi.
Assumptions: The loading is static. The member 2 can be approximated as a simple beam with an overhang.
See Figures 3.31 (page 136) and 4.11 and Table A.9
Member 3.The elongation of this tensile link(Figure 3.31a)is obtained from Equation 4.1.
So, due to symmetry in the assembly, the displacement of each end point A is
\delta = \frac {PL} {AE} (4.1)
\begin{aligned} \delta_A &=\frac{1}{2}\left(\frac{P L}{A E}\right)=\frac{F_A L_3}{2 A E} \\ &=\frac{128(1.25)}{2\left(\frac{3}{8}\right)\left(\frac{1}{8}\right)\left(30 \times 10^6\right)}=56.9\left(10^{-6}\right) in . \end{aligned}
Member 2. This jaw is loaded as shown in Figure 3.31b. The deflection of point D is made up of two parts: a displacement υ_{1} owing to bending of part DA acting as a cantilever beam and a displacement υ_{2} caused by the rotation of the beam axis at A (Figure 4.11). The deflection υ_{1} at D (by case 1 of Table A.9) is
\upsilon _{1}=\frac{Q a^3}{3 E I}
The angle \theta _{A} at the support A (from case 7 of Table A.9) is
\theta_A=\frac{M b}{3 E I}
where M = Qa. The displacement υ_{2} of point D, due to only the rotation at A, is equal to \theta _{A} a, or
\upsilon _{2}=\frac{Q b a^2}{3 E I}
The total deflection of point D, shown in Figure 4.11, υ_{1} + υ_{2}, is then
\upsilon _{D}=\frac{Q b a^2}{3 E I}(a+b)
In the foregoing, we have
\begin{aligned} I &=\frac{1}{12} t_2 h_2^3 \\ &=\frac{1}{12}\left(\frac{3}{16}\right)\left(\frac{3}{8}\right)^3=0.824\left(10^{-3}\right) \text { in. }^4 \end{aligned}
Substitution of the given data results in
\upsilon _D=\frac{96\left(1^2\right)(1+3)}{3\left(30 \times 10^6\right)\left(0.824 \times 10^{-3}\right)}=5.18 \times 10^{-3} \text { in. }
Comment: Only very small deflections are allowed in members 2 and 3 to guarantee the proper cutting stroke, and the values found are acceptable.
