Problems on cantilever beams
1)
Step 1: Calculation of shear force
Shear force at point of 500N = 500N
Shear force at point of 800N = 500+800= 1300N
Shear force at point of 300N = 500+800+300=1600N
Shear force at point of 400N = 500+800+300+400=2000N
Shear force at point of fixed point A = 500+800+300+400=2000N
Step 2: Calculation of Bending Moment
Bending Moment at point of 500N = 0N-m(Note: this is end pont of beam where beyond this point there is no force existed)
Bending Moment at point of 800N = 500X0.5= -250N-m
Bending Moment at point of 300N = -500X1-800X0.5= -900N-m
Bending Moment at point of 400N = -500X1.5-800X1-300X0.5= -1700N-m
Bending Moment at fixed point A= -500X2-800X1.5-300X1-400X0.5= -2700N-m
2)
Step 1: Calculation of shear force
Shear force at point of 800N = 800N
Shear force at point of 500N = 500+800= 1300N
Shear force at point of 300N = 500+800+300=1600N
Shear force at point of fixed point A = 500+800+300=1600N
Step 2: Calculation of Bending Moment
Bending Moment at point of 800N = 0N-m(Note: this is end pont of beam where beyond this point there is no force existed)
Bending Moment at point of 500N = 800X0.8= -640N-m
Bending Moment at point of 300N = -800X1.5-500X0.7= -1550N-m
Bending Moment at fixed point A= -800X2-500X1.2-300X1-300X0.5= -2350N-m
3)
Step 1: Calculation of shear force
Shear force at point of 3KN = 3KN
Shear force at point of 2KN = 3+2= 5KN
Shear force at point of 1KN = 3+2+1=6KN
Shear force at point of fixed point A = 3+2+1=6KN
Step 2: Calculation of Bending Moment
Bending Moment point of 3KN = 0N-m(Note: this is end pont of beam where beyond this point there is no force existed)
Bending Moment at point of 2KN = -3X2= -6KN-m
Bending Moment at point of 1KN = -3X3-2X1= -11KN-m
Bending Moment at fixed point A= -3X4-2X2-1X1=-17KN-m
4)
Step 1: Calculation of shear force
Shear force at point B= 0
Shear force at point of fixed point A = 10 X 2.5=25KN
Step 2: Calculation of Bending Moment
Bending Moment at point B= 0 N-m(Note: this is end point of beam where beyond this point there is no force existed)
Bending Moment at fixed point A= 10 X 2.5 X 2.5/2 = -31.25 KN-m
5)
Step 1: Calculation of shear force
Shear force at point C= 0
Shear force at point B=3KN
Shear force at point of fixed point A = 3KN
Step 2: Calculation of Bending Moment
Bending Moment at point C= 0 N-m(Note: this is end point of beam where beyond this point there is no force existed)
Bending Moment at point B=2X1.5X0.75=-2.25 KN-m
Bending Moment at fixed point A= 2 X 1.5 X(0.75+0.5)= -3.75 KN-m
6)
Step 1: Calculation of shear force
Shear force at point B= 3KN
Shear force at point of fixed point A = 4+3=7 KN
Step 2: Calculation of Bending Moment
Bending Moment at point B= 0 N-m(Note: this is end point of beam where beyond this point there is no force existed)
Bending Moment at fixed point A= -(3 X 2)-(2 X 2 X 1) = -10 KN-m
7)
Step 1: Calculation of shear force
Shear force at point D = 8KN
Shear force at point C= 15+8= 23KN
Shear force at point B= 15+8= 23KN
Shear force at point of fixed point A =4X2+8+15=31KN
Step 2: Calculation of Bending Moment
Bending Moment at point D= 0KN-m(Note: this is end pont of beam where beyond this point there is no force existed)
Bending Moment at point C = -(8X2)= -16KN-m
Bending Moment at point B = -(8X3)-(15X1)= -39KN-m
Bending Moment at fixed point A= -(8X5)-(15X3)-(8X1)= - 93KN-m
8)
Step 1: Calculation of shear force
Shear force at point C =0KN
Shear force at point B= 2+1.5X0.5=2.75KN
Shear force at point of fixed point A =2+1.5X2=5KN
Step 2: Calculation of Bending Moment
Bending Moment at point C= 0KN-m(Note: this is end pont of beam where beyond this point there is no force existed)
Bending Moment at point B = -(1.5X0.5X0.25)= -0.1875KN-m
Bending Moment at fixed point A= -(1.5X2X1)-(2X1.5)= -6KN-m
9)
Step 1: Calculation of shear force
Shear force at point D = 0KN
Shear force at point C= 3+(2X0.25)=3.5KN
Shear force at point B= 2X1.25+3=5.5KN
Shear force at point of fixed point A =5.5KN
Step 2: Calculation of Bending Moment
Bending Moment at point D= 0KN-m(Note: this is end pont of beam where beyond this point there is no force existed)
Bending Moment at point C = -(2X0.25X0.25/2)= -0.0625KN-m
Bending Moment at point B = -(3X1)-(2X1.25X1.25/2)= -4.5625KN-m
Bending Moment at fixed point A= -(3X1.25)-(2X1.25X(1.25/2+0.25))= - 5.9375KN-m
10)
Step 1: Calculation of shear force
Shear force at point E = 2.5KN
Shear force at point D= 2.5KN
Shear force at point C= 2.5+1X2=4.5KN
Shear force at point B= 2.5+1X2+3=7.5KN
Shear force at point of fixed point A =7.5KN
Step 2: Calculation of Bending Moment
Bending Moment at point E= 0KN-m(Note: this is end pont of beam where beyond this point there is no force existed)
Bending Moment at point D = -(2.5X0.5)= -1.25KN-m
Bending Moment at point C= -(2.5X2.5)-(2X1)= -8.25KN-m
Bending Moment at point B= -(2.5X4)-(2X2.5)= -15KN-m
Bending Moment at fixed point A= -(2.5X5)-(2X3.5)-(3X1)= - 22.5KN-m
11)
Step 1: Calculation of shear force
Shear force at point D= 20KN
Shear force at point C=20+10=30KN
Shear force at point B=20+10+2(12) =69KN
Shear force at point of fixed point A =69KN
Step 2: Calculation of Bending Moment
Bending Moment at point D= 0KN-m(Note: this is end pont of beam where beyond this point there is no force existed)
Bending Moment at point C = -(20X2)= -40KN-m
Bending Moment at point B= -(2.0X4)-(10X2)-24= -124KN-m
Bending Moment at fixed point A= -(20X5)-(10X3)-(24X2)-15= - 193KN-m
12)
Step 1: Calculation of shear force
Shear force at point E = 2KN
Shear force at point D= 2KN
Shear force at point C= 20+2=22KN
Shear force at point B= 3+22=25KN
Shear force at point of fixed point A =25KN
Step 2: Calculation of Bending Moment
Bending Moment at point E= 0KN-m(Note: this is end pont of beam where beyond this point there is no force existed)
Bending Moment at point D = -(2X0.5)= -1KN-m
Bending Moment at point C= -(2X2.5)-(20X1)= -25KN-m
Bending Moment at point B= -(2X4)-(20X2.5)= -58KN-m
Bending Moment at fixed point A= -(2X5)-(20X3.5)-(3X1)= - 83KN-m
13)
Step 1: Calculation of shear force
Shear force at point B=0KN
Shear force at point of fixed point A =10KN
Step 2: Calculation of Bending Moment
Bending Moment at point B= 0KN-m
Bending Moment at fixed point A= -(1/2X5x4)(1/3X4)= - 13.33KN-m
14)
Step 1: Calculation of shear force
Shear force at point F = 0KN
Shear force at point E= 15KN
Shear force at point D=15KN
Shear force at point C= 15KN
Shear force at point B= 15+10=25KN
Shear force at point of fixed point A =25KN
Step 2: Calculation of Bending Moment
Bending Moment at point F= 0KN-m(Note: this is end pont of beam where beyond this point there is no force existed)
Bending Moment at point E = 0KN-m
Bending Moment at point D= -(15X0.5)-20= -27.5KN-m
Bending Moment at point C= -(15X1)= -15KN-m
Bending Moment at point B= -(15X1.5)-(10X0.25)= -25KN-m
Bending Moment at fixed point A= -(15X2)-(10X0.75)= - 37.5KN-m
15)
Step 1: Calculation of shear force
Shear force at point B=0KN
Shear force at point of fixed point A =12KN
Step 2: Calculation of Bending Moment
Bending Moment at point B= 0KN-m
Bending Moment at fixed point A= -(1/2X6x4)(1/3X4)= - 24KN-m
16)
Step 1: Calculation of shear force
Shear force at point B=0KN
Shear force at point of fixed point A=2+1(4) =6KN
Step 2: Calculation of Bending Moment
Bending Moment at point B= 0KN-m
Bending Moment at fixed point A= -(2X4)-(1X4X2)= - 16KN-m
17)
Step 1: Calculation of shear force
Shear force at point B=3 KN
Shear force at point C = 3 KN
Shear force at point of fixed point A=3+1(2)+2 =7 KN
Step 2: Calculation of Bending Moment
Bending Moment at point B= 0KN-m
Bending Moment at point C= 3X4=12KN-m
Bending Moment at fixed point A= -(3X6)-(1X2X1)-(2X1)= - 22KN-m
18)
Step 1: Calculation of shear force
Shear force at point D= 0KN
Shear force at point C=0.5X2X20=20KN
Shear force at point B=20+30 =50KN
Shear force at point of fixed point A =50KN
Step 2: Calculation of Bending Moment
Bending Moment at point D= 0KN-m(Note: this is end pont of beam where beyond this point there is no force existed)
Bending Moment at point C = -(0.5X20X2X1/3(2))= -13.33KN-m
Bending Moment at point B= -(0.5X20X2X(1/3(2)+1)))+(100)= -66.66N-m
Bending Moment at fixed point A= -(0.5X20X2X(1/3(2)+3)-(30X2)= - 133.33KN-m
19)
Step 1: Calculation of shear force
Shear force at point E= 0KN
Shear force at point D=0KN
Shear force at point C= 20KN
Shear force at point B= 20+10=30KN
Shear force at point of fixed point A =30KN
Step 2: Calculation of Bending Moment
Bending Moment at point E= 0KN-m(Note: this is end pont of beam where beyond this point there is no force existed)
Bending Moment at point D= 100= 100KN-m
Bending Moment at point C= 0KN-m
Bending Moment at point B= -(20X1)= -20KN-m
Bending Moment at fixed point A= -(20X2)-(10X1)= - 50KN-m
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