A timber column, 3 m high, has a rectangular cross section, 100 mm × 200 mm, and is reinforced over its complete length by two steel plates each 200 mm wide and 10 mm thick attached to its 200 mm wide faces. The column is designed to carry a load of 100 kN. If the failure stress of the timber is 55

Question

A timber column, 3 m high, has a rectangular cross section, 100 mm×200 mm, and is reinforced over its complete length by two steel plates each 200 mm wide and 10 mm thick attached to its 200 mm wide faces. The column is designed to carry a load of 100 kN. If the failure stress of the timber is 55 N/mm² and that of the steel is 380 N/mm² , check the design using a factor of safety of 3 for the timber and 2 for the steel. E (timber) = 15 000 N/mm² , E (steel) = 200 000 N/mm².

Accepted Answer

This problem is very similar to P.7.14 and so the same equations may be used directly to obtain a solution. From Eqs (7.38)

[latex]\sigma_{ S }=\frac{E_{ S }}{A_{ C } E_{ C }+A_{ S } E_{ S }} P \quad \sigma_{ C }=\frac{E_{ C }}{A_{ C } E_{ C }+A_{ S } E_{ S }} P[/latex] (7.38)

[latex] \sigma_{ ext {tim }}=\frac{1000 imes 10^{3} imes 15000}{[(100 imes 200) 15000+(2 imes 200 imes 10) 200000]} [/latex]

i.e.

[latex] \sigma_{ ext {timber }}=13.6 N / mm ^{2} [/latex]

The allowable stress in the timber is 55/3=18.3 N/mm² so that the timber size is satisfactory. Also

[latex] \sigma_{ st }=\frac{1000 imes 10^{3} imes 200000}{[(100 imes 200) 15000+(2 imes 200 imes 10) 200000]} [/latex]

i.e.

[latex] \sigma_{ ext {steel }}=181.8 N / mm ^{2} [/latex]

The allowable stress in the steel is 380/2=190 N/mm² so that the size of the steel plates is satisfactory.

Question 7.15: A timber column, 3 m high, has a rectangular cross section, ...

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