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ENGR5004 / Week 4
Old spec Statics Session 8 ExampleTutorialOld spec ENGR2162:28 min

ENGR216 (old spec) Statics session 8 worked example (slides 8-9) official answers

A beam is made of three equal planks, each of cross section a×ba \times b with a=100a = 100 mm and b=20b = 20 mm, nailed together into an I section: two horizontal flanges (aa wide, bb thick) and a vertical web (bb thick, aa deep) between them. The nails joining each flange to the web are spaced at z=25z = 25 mm along the beam and the vertical shear in the beam is V=500V = 500 N. Determine the shearing force in each nail.

I section of three planks: flanges a wide and b thick, web b thick and a deep between them, nailed through the flanges into the web.
I section of three planks: flanges a wide and b thick, web b thick and a deep between them, nailed through the flanges into the web.
Formulas you may need
  • Shear flow (horizontal force per unit length) q=VQIq = \dfrac{VQ}{I}; nail force F=qzF = qz (learn this; τ=VQ/(It)\tau = VQ/(It) is on the formula sheet)
  • First moment of area Q=yˉAQ = \bar y A of the area beyond the cut, about the neutral axis (on the formula sheet)
  • Rectangle I=bh312I = \dfrac{bh^3}{12} and the parallel axis theorem I=Iˉ+Ad2I = \bar I + Ad^2 (on the formula sheet)