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Engineering

Montgomery College Rockville Campus

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A simply supported beam is covered with snow resulting in the distributed load shown. find
the functions of the shear and bending moments as functions of x along the beam. Consider
point C to be like a hinge, point B a long thin vertical link, and point A cantilevered. (I already solve it but it has few mistakes I want to be corrected)

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ES102 Statics Group Problem 12 A simply supported beam is covered with snow resulting in the distributed load shown. find the functions of the shear and bending moments as functions of x along the beam. Consider point C to be like a hinge, point B a long thin vertical link, and point A cantilevered. 400 N/m A B 1.5 m C 3.5 m A 1) Whole System: y wmax= 400 N/m A x 1.5 m 3.5 m FB ∑ F x= F B F C −3.5m w max − 12 1.5m wmax =0 1 1 3.5m w max 3.5m 1.5m [ 1.5m w max ]=0 ∑ M C =−3.5m F B 3.5 2 3 2 3.5 1 1 3.5m w max 3.5m 1.5m[ 1.5m w max ] 2 3 2 F B= =1043N 3.5m 1 F C =−F B 3.5m w max  1.5m w max =657.1 N 2 FC 2) Choose origin at A. 3) Cut a section between A and B. Note that the load function w(x) is an equation of a straight line with a y-intercept of 0. w w  x = max x y 1.5m ∑ F x =−V  x− 12 x w x =0 Mb w max 1 A x V  x =− x x 2 1.5m V 1 N 2 x V  x =−133 x 3 m2   ∑ M section =M b  x  13 x 12 x w  x =0  w max 1 1 M b  x =− x x x 3 2 1.5m 1 N 3 M b  x =−400 x 9 m2  Cut the section between B and C. Note that the load function w(x) is now constant. wmax= 400 N/m y Mb x A V 1.5 m x FB ∑ F x =−V  x− 12 1.5m wmax  F B− x−1.5m w max =0 1 V  x =− 1.5m w max  F B − x−1.5m w max 2 N N V  x =−300N1043N− x400 600N=1343N− x400 m m ∑ M section =M b  x  x− 23 1.5m  12 1.5m w max  12  x−1.5m  x−1.5m w max − x−1.5m  F B=0 2 1 1 M b  x = x−1.5m 1043N− x− 1.5m  1.5m w max −  x−1.5m x−1.5m w max 3 2 2 N M b  x =−1565Nm1043N x300Nm−300N x−200 x 2 600N x−450Nm m N M b  x =−1715Nm1343N x−200 x 2 m ES102 Statics Group Problem 12 A simply supported beam is covered with snow resulting in the distributed load shown. find the functions of the shear and bending moments as functions of x along the beam. Consider point C to be like a hinge, point B a long thin vertical link, and point A cantilevered. 400 N/m A B C 1.5 m 3.5 m 1) Load as a function of x, w(x) . w(x) A A x 1.5 m 3.5 m 2) Shear as a function of x, V(x) FC FB 1000 800 600 V (N) 400 200 FB 0 -200 0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.5 1.7 1.9 2.1 2.3 2.5 2.7 2.9 3.1 3.3 3.5 3.7 3.9 4.1 4.3 4.5 4.7 4.9 -400 FC -600 -800 x (m) 3) Bending Moment as a function of x, M(x) Position of maximum bending moment 600 500 M (Nm) 400 300 200 100 0 -100 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.5 1.7 1.9 2.1 2.3 2.5 2.7 2.9 3.1 3.3 3.5 3.7 3.9 4.1 4.3 4.5 4.7 4.9 x 0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 5 -200 x (m)
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