30 



STRENGTH OF MATERIALS 



Problem 29. What force will pull the head off the bolt in Problem 28, if the 

 head is of the same thickness as the nut ? 



Problem 30. A f-in. rivet connects two plates which transmit a tension <>f 

 2500 Ib. Assuming that the shear is uniformly distributed over the cross section 

 of the rivet, find the unit shear on the rivet. 



Problem 31. An eyebar is designed to carry a load of 16 tons. What must 

 be the size of the pin to be safe against shear ? 



NOTE. Consider the pin in double shear, and assume that this shear is uniformly 

 distributed over the cross section of the pin. 



34. Relation between the elastic constants. Suppose a cube is 

 subjected to compressive stress on one pair of opposite faces and 



tensile stress on another pair 

 of opposite faces. Then, if 1 1 1 * 

 axes of X and Y are drawn 

 c in the direction of the strain, 



P X = P,', and the strain is 

 one of simple shear, as ex- 

 plained in Article 31. 



Let x denote the length 

 of an edge of the cube before 

 strain. Under the strain tin* 

 cube becomes a parallel .ja- 

 ped, its increase in length 

 in the direction of the X-axis, due to the tensile stress p xt being 



-^; and its increase in length in this direction, due to the com- 

 pressive stress p xt being -** 



Therefore, if dx denotes the total increase in length in the direc- 

 tion of the X-axis, 



FIG. 17 



or, since p x = a, 



E mE 



By reason t>f the strain the angle between the diagonals is 

 increased by an amount <, and therefore the angle between a 



diagonal and a side is increased by J. From the right triangle 

 ABC (Fig. 17), a 



