JOINTS AND CONNECTIONS 



197 



a bending moment is set up at a joint where all the members are 

 rigidly connected and that the other ends of the members are 

 likewise rigidly connected. The members are bent at their ends 

 in opposite directions, 



? /N B Center of Gravity 

 V /^"^ 2 If. 6\4\*f 



thus setting up a double 

 curvature, with a point 

 of contraflexure, or 

 point of zero moment 

 in the middle of the 

 length. The members 

 may be considered as 

 beams fastened at the 

 joint with the middle 

 point the free end. All 

 the members, therefore, 



4rta*7.2.'f** 



\ Direct comp.6SOOO!b ; 

 orSOOffJbpersa in. 



Fig. 115. 



resist the bending moment in proportion to their relative rigidities. 

 The angular displacement of the joint is the same for all the 

 members meeting at the joint. The angular displacement at 

 the joint then is the deflection of the middle point of any member 

 divided by the half length of that member. This can be demon- 

 strated by an expression in which appears the modulus of elas- 

 ticity, the bending moment, the moment of inertia, the half length 

 and the angular displacement. Dropping all the factors common 

 to all the members there are left only the Moment of Inertia and 

 the half length, so it is readily seen that the total bending mo- 

 ment is divided among the several members in proportion to their 



respective rigidities, that is in proportion to y The Moment of 



Inertia is in inches and the half length should properly be in 

 inches. However fewer figures are used and the work simplified 

 by dividing the Moment of Inertia by the total length of the 

 member in feet. The proportionate values are the same. This 

 will be illustrated. 



Let the total length of the chord between joints be 12 ft. and 

 the depth between centers of gravity be 6 ft. The length of the 

 diagonals will be 8.24 ft. but in the division we will use only 8 ft. 

 The Moment of Inertia of the top chord is 27, the value for one 

 angle being 13.5, as shown on page 148, Carnegie, 1913 ed.. and on 

 page 113, Jones & Laughlin, 1916 ed., similar values being given 

 in the other standard steel handbooks. Similarly the Moment 



