Solution Found!
The simply-supported beam is built-up from three boards by
Chapter 7, Problem 7-40(choose chapter or problem)
The simply-supported beam is built-up from three boards by nailing them together as shown. The wood has an allowable shear stress of \(\tau_{\text {allow }}=1.5 \ \mathrm{MPa}\), and an allowable bending stress of \(\sigma_{\text {allow }}=9 \ \mathrm{MPa}\). The nails are spaced at s = 75 mm, and each has a shear strength of 1.5 kN. Determine the maximum allowable force P that can be applied to the beam.
Questions & Answers
QUESTION:
The simply-supported beam is built-up from three boards by nailing them together as shown. The wood has an allowable shear stress of \(\tau_{\text {allow }}=1.5 \ \mathrm{MPa}\), and an allowable bending stress of \(\sigma_{\text {allow }}=9 \ \mathrm{MPa}\). The nails are spaced at s = 75 mm, and each has a shear strength of 1.5 kN. Determine the maximum allowable force P that can be applied to the beam.
ANSWER:
Using the Moment-Area Method, we can calculate the maximum allowable force P.
First, calculate the flexural stiffness of the beam, EI:
EI = 3 x (12 x 10^3) x (75 x 10^-3)^3 /(3 x 2 x