Answer to Question #167501 in Mechanics | Relativity for Sage Topaz

Question

A sagging floor is jacked up and a steel girder 10.0 feet long whose cross-sectional area is 6.0 inches² is put in place underneath. when a jack is removed, a sensitive strain gauge that shows that the girder has been compressed by 0.0080 inches. Find the load the girder is supporting. (change everything to metric system units and use metric system units)

Answer 1

Let l = 10 ft = 3.05 m - the lenght of the girder;

A = 6.0 in² = 0.0039 m² - the cross-sectional area of the girder;

$\Delta l$ = 0.008 in = 0.0002 m - the compression of the girder;

E = 200 GPa - the Young modulus of steel.

The load the girder is supporting:

$G=\sigma A=E\varepsilon A=\frac {E\Delta lA}{l} =\frac {200\cdot 10^9\cdot 0.008\cdot 0.0002}{3.05}\approx100 kN$

Answer: 100 kN.