I 7 i.] 



JOINTED FRAMES. 



IO I 



where a = 



If, however, the weight w of the 

 rod DE cannot be neglected, we 

 have at D a horizontal reaction D x 

 and a vertical reaction D v . The 

 equilibrium of DE requires that 



zD,, = w. Hence resolving and 



. . y , , - , 



taking moments as before, we find 



p . 



169. Exercise. 



(i) Two homogeneous rods AC, BC of equal weight, but unequal 

 length, are hinged together at C while their other ends are attached to 

 fixed hinges A, B in the same vertical line. Show that the line of action 

 of the reaction at C bisects AB. 



170. A triangular frame formed of rigid rods is rigid as a 

 whole, even when the connections are pin-joints. A quadran- 

 gular frame with pin-joints becomes rigid only by the insertion 

 of a diagonal. 



The iron and steel trusses 'used for roofs and bridges gener- 

 ally consist of a system of triangles, or quadrangles with diago- 

 nals, so that the whole truss can be regarded as one rigid body, 

 at least in first approximation. 



Any one rod, or member, of the frame-work is thus acted upon 

 by two equal and opposite forces, i.e, by a stress, in the direction 

 of its length, the external forces, including the proper weight, 

 being regarded as applied at the joints only. If the stress be a 

 tension, i.e. if the forces tend to stretch or elongate the mem- 

 ber, the latter is called a tie; a member subject to compression 

 or crushing is called a strut. 



171. For the purpose of dimensioning the members, it is 

 necessary to know the stress in every member. The following 



