BENDING-MOMENT AND SHEAR DIAGRAMS 47 



To obtain the shear diagram, start at the left end and lay off the reaction of 

 2400 Ib. upward. Since the load is 200 lb./ft., at 4 ft. from the left end the shear 

 will be 2400- 4 x 200 = 1600 Ib. As we pass this point the concentrated load of 1 ton 

 will cause the shear to drop to 1600 - 2000 = - 400 Ib. The shear then continues 

 to drop 200 lb./ft., until at the right support it becomes 400 8 x 200 = 2000 Ib. 

 As this point is passed, the reaction, which is equivalent to a concentrated load of 

 2800 Ib. upward, causes the shear to change suddenly to 2000 + 2800 = 800 Ib. 

 It then gradually drops again and becomes zero at the end of the beam. 



On account of the uniform load the moment diagram will be segments of para- 

 bolas. To plot these parabolas the values of the moment at a number of points 

 along the beam may be calculated. Thus, at points 2, 4, 10, 12, and 14 ft. from the 

 left end the moments are 



M 2 = 2400 2 - 400 . 1 = 4400 f t.-lb. 



M 4 = 2400 . 4 800 . 2 - 8000 f t.-lb. 



M w = 2400 . 10 - 2000 5 - 2000 . 6 = 2000 f t.-lb. 



M 12 = 2400 12 - 2400 6 - 2000 . 8 = - 1600 f t.-lb. 



M u = 2400 14 - 2800 . 7 - 2000 . 10 = - 400 f t.-lb. 



The maximum moment is evidently at the 1-ton load, and the maximum shear at 

 the left support. 



77. A simple beam 10 ft. long is supported at the ends and carries a load of 

 800 Ib. at a point 4 ft. from the left end. Draw the shear and moment diagrams. 



78. A simple beam 20 ft. long, supported at the ends, carries a uniform load of 

 50 lb./ft. and a concentrated load of 600 Ib. at 5 ft. from the right end. Draw 

 the shear and moment diagrams. 



79. A simple beam of 15 ft. span is supported at the ends and carries a uniform 

 load of 100 lb./ft. and concentrated loads of 500 Ib. at 4 ft. from the left end and 

 1000 Ib. at 8 ft. from the left end. Plot the shear and moment diagrams. 



80. A simple beam of 16ft. span carries concentrated loads of 2001b.,~4001b., 

 and 100 Ib. at distances of 4 ft., 8 ft., and 12 ft., respectively, from the left support. 

 Neglecting the weight of the beam itself, sketch the shear and moment diagrams. 



81. A simple beam of 9 ft. span carries a total uniform load of 400 Ib. over the 

 middle third of the span. Neglecting the weight of the beam, draw the shear and 

 moment diagrams for this loading. 



82. The total load on a car axle is 8 tons, equally divided between the two 

 wheels. Distance between centers of wheels is 4^ ft., and distance between centers 

 of journals is 5^ ft. Draw the shear and moment diagrams for the axle so loaded. 



83. Draw the shear and moment diagrams for a simple beam 10 ft. long, bear- 

 ing a total uniform load of 100 lb./ft. and concentrated loads of 1 ton at 4 ft. from 

 the left end and 2 tons at 3 ft. from the right end. 



84. A beam 12 ft. long is supported at the ends and carries loads of 4000 Ib. 

 and 1000 Ib. at 2 ft. and 4 ft., respectively, from the left end. No uniform load. 

 Sketch the shear and moment diagrams. 



85. A beam 20 ft. long, supported at the ends, bears a uniform load of 100 lb./ft. 

 extending from the left end to the center, and a concentrated load of 1000 Ib. at 

 5 ft. from the right end. Plot the shear and moment diagrams. 



86. A beam 16 ft. long, supported at the ends, carries a uniform load of 200 lb./ft. 

 extending 10 ft. from the left end, and concentrated loads of 1 ton and ^ ton at 8 ft. 

 and 12 ft., respectively, from the left end. Draw the shear and moment diagrams. 



