If the small strain tensor at a point in a body made of a moldable plastic could be determined experimentally by measuring the unit extensions in six directions at the point (the coordinate directions and the three directions bisecting the angles between the axes: em for the direction between X1 and X2, en between X2 and X3, et between X3 and X1), determine the shear strain components E12, E23, and E31 in terms of the six measured unit extensions.

Afoot bridge is made as a simple deck, 4 m long, with a cross section 2 m (wide) and 20 cm thick, and made of wood. the deck is supported at the two ends. the maximum load allowable on the bridge is 10 tons, provided it is uniformly distributed on the deck. to sense this load, a strain gauge is placed at the center of the bridge and its resistance is monitored. if the sensor has a nominal resistance of 350 s2 and a gauge factor of 3.6, what is the reading of the strain gauge at maximum load? the modulus of elasticity for the wood used in the construction is 10 gpa.