90 



HANDBOOK OF MECHANICAL DESIGN 

 CHART FOR DETERMINING BENDING MOMENTS 



/¥ 



'^ 



-12 



Various Conditions of Loading 



Y"^ Uniform load. Fixed ends 

 ■^ Load of center, fixed ends 



>i 



100,000- 

 90,000- 

 80,000 - 

 70,000- 



60,000 - 



50,000 - 



40,000- 



30,000 — 



20,000 — 



■ i>>""ii^/i//i,/,,M Uniform load, supp. and fixed ends 



d^ I Y"""'"'"'^'''^ Uniform load,supported ends 



'•" III ^ Load increasing to one end 



6-«---B=22Z^2&»^ Load increasing to center 



''"r '-— 7~l Load at center, supp. and fixed ends 



4. T P^-2 -^ 



Example 



Cantilever beam 

 with concentrated 



load P= 2,000 lb. 



atend.L=50in. 



C=l 



—^ Load at center, supported ends 

 Load increasing to fixed end 



7- ,-rrr7777Z^ 



C kL-iz 2rL-H j^Q svrr.metrical and equal loads 

 ' i T 



10,000 — 

 9,000 

 8,000 

 7,000 

 6,000 

 5,000 

 4,000 — 



3,000 — 



2,000 - 



\ i,,/iij,,j,iii...ii.^ Uniform load, one fixed end 



P P 



I rj 2 \ Two symmetrical and cquol loads 



X 



-| Concentroted load at free en^ 



^-- Turning scale 



-20 



-30 



-40 

 -50 

 -60 



-80 

 - 100 



— 200 



•300 



■400 

 -500 



cu = uniform load per unit length 

 P = concentrated load,use P lb.= W lb. 

 L = total span in inches unless 



otherwise shown 

 W= wL 



I- 

 Join CandL extend W-TtoM 

 M - 100,000 



600 



800 

 1,000 



— 2,000 



• 3,000 



■ 4,000 



• 5,000 



■ 6,000 

 8,000 



3 



X 



10,000 



300-^ 



200 — 



100- 

 90- 

 80- 

 70 - 

 60 - 

 50- 

 40 — 



BO- 



ZO-^ 



10 

 9 — 



7 — 

 6— ' 



c 



E 

 o 



— - 20,000 ;;: 



■ 30,000 



■ 40,000 

 • 50,000 



■ 60,000 .E 



" 80,000 c 



100,000 CO 



E 



E 



200,000 S 



o 



300,000 ^ 

 400000 ^ 

 500,000 

 600,000 



800,000 

 1,000000 



2000,000 



3,000,000 



4,000,000 

 5,000,000 

 6,000,000 

 8,000,000 

 10,000,000 



20,000,000 



30,000,000 

 40,000,000 

 50,000,000 



