SHEAR FORCE AND BENDING MOMENT
Definition:
Shear force: The force which tend to shear off the section and is obtained as the algebraic sum of all forces including the reactions acting normal to the axis of the beam either to the left or right of the beam.
Sign convention
Positive Shear Force
Negative Shear Force
Sign convention for shear force in brief
Direction

Positive SF

Negative SF

Left side

Upward force

Downward force

Right side

Downward force

Upward force

Bending moment: The algebraic sum of all the moments of the forces and reactions in a beam towards either left side or right side of the support is known as bending moment.
Types of bending moment:
Sagging bending moment: The moment about the point which produces convexity below the centre line is called as sagging bending moment. It is also called as positive bending moment.
Consider the simply supported beam with central concentrated load “F”. The moment due to the force F produces a deflection in the downward direction which in turn results in the formation of sagging bending moment.
Hogging bending moment: The moment about the point which produces convexity above the centre line is called as hogging bending moment. It is also called as negative bending moment.
Consider the simply supported beam with central concentrated load “F”. The moment due to the force F produces a deflection in the upward direction which in turn results in the formation of hogging bending moment.
Differences between sagging and hogging bending moment
Sagging bending moment

Hogging bending moment

The moment about the point which produces convexity below the centre line is called as sagging bending moment.

The moment about the point which produces convexity above the centre line is called as hogging bending moment.

It is also termed as positive bending moment

It is also termed as negative bending moment

Top fibres of beam are subjected to compression.

Top fibers of beam are subjected to tension.

Bottom fibers of beam are subjected to tension.

Bottom fibers of beam are subjected to compression.

Sign conventions for bending moments
Direction

Positive BM

Negative BM

Left side

Clock wise

Anti Clock wise

Right side

Anti Clock wise

Clock wise

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 = 0Nm(Note: this is end pont of beam where beyond this point there is no force existed)
Bending Moment at point of 800N = 500X0.5= 250Nm
Bending Moment at point of 300N = 500X1800X0.5= 900Nm
Bending Moment at point of 400N = 500X1.5800X1300X0.5= 1700Nm
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 = 0Nm(Note: this is end pont of beam where beyond this point there is no force existed)
Bending Moment at point of 500N = 800X0.8= 640Nm
Bending Moment at point of 300N = 800X1.5500X0.7= 1550Nm
Bending Moment at fixed point A= 800X2500X1.2300X1300X0.5= 2350Nm
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 = 0Nm(Note: this is end pont of beam where beyond this point there is no force existed)
Bending Moment at point of 2KN = 3X2= 6KNm
Bending Moment at point of 1KN = 3X32X1= 11KNm
Bending Moment at fixed point A= 3X42X21X1=17KNm
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 Nm(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 KNm
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 Nm(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 KNm
Bending Moment at fixed point A= 2 X 1.5 X(0.75+0.5)= 3.75 KNm
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 Nm(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 KNm
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= 0KNm(Note: this is end pont of beam where beyond this point there is no force existed)
Bending Moment at point C = (8X2)= 16KNm
Bending Moment at point B = (8X3)(15X1)= 39KNm
Bending Moment at fixed point A= (8X5)(15X3)(8X1)=  93KNm
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= 0KNm(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)= 0.1875KNm
Bending Moment at fixed point A= (1.5X2X1)(2X1.5)= 6KNm
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= 0KNm(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)= 0.0625KNm
Bending Moment at point B = (3X1)(2X1.25X1.25/2)= 4.5625KNm
Bending Moment at fixed point A= (3X1.25)(2X1.25X(1.25/2+0.25))=  5.9375KNm
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= 0KNm(Note: this is end pont of beam where beyond this point there is no force existed)
Bending Moment at point D = (2.5X0.5)= 1.25KNm
Bending Moment at point C= (2.5X2.5)(2X1)= 8.25KNm
Bending Moment at point B= (2.5X4)(2X2.5)= 15KNm
Bending Moment at fixed point A= (2.5X5)(2X3.5)(3X1)=  22.5KNm
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= 0KNm(Note: this is end pont of beam where beyond this point there is no force existed)
Bending Moment at point C = (20X2)= 40KNm
Bending Moment at point B= (2.0X4)(10X2)24= 124KNm
Bending Moment at fixed point A= (20X5)(10X3)(24X2)15=  193KNm
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= 0KNm(Note: this is end pont of beam where beyond this point there is no force existed)
Bending Moment at point D = (2X0.5)= 1KNm
Bending Moment at point C= (2X2.5)(20X1)= 25KNm
Bending Moment at point B= (2X4)(20X2.5)= 58KNm
Bending Moment at fixed point A= (2X5)(20X3.5)(3X1)=  83KNm
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= 0KNm
Bending Moment at fixed point A= (1/2X5x4)(1/3X4)=  13.33KNm
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= 0KNm(Note: this is end pont of beam where beyond this point there is no force existed)
Bending Moment at point E = 0KNm
Bending Moment at point D= (15X0.5)20= 27.5KNm
Bending Moment at point C= (15X1)= 15KNm
Bending Moment at point B= (15X1.5)(10X0.25)= 25KNm
Bending Moment at fixed point A= (15X2)(10X0.75)=  37.5KNm
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= 0KNm
Bending Moment at fixed point A= (1/2X6x4)(1/3X4)=  24KNm
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= 0KNm
Bending Moment at fixed point A= (2X4)(1X4X2)=  16KNm
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= 0KNm
Bending Moment at point C= 3X4=12KNm
Bending Moment at fixed point A= (3X6)(1X2X1)(2X1)=  22KNm
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= 0KNm(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))= 13.33KNm
Bending Moment at point B= (0.5X20X2X(1/3(2)+1)))+(100)= 66.66Nm
Bending Moment at fixed point A= (0.5X20X2X(1/3(2)+3)(30X2)=  133.33KNm
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= 0KNm(Note: this is end pont of beam where beyond this point there is no force existed)
Bending Moment at point D= 100= 100KNm
Bending Moment at point C= 0KNm
Bending Moment at point B= (20X1)= 20KNm
Bending Moment at fixed point A= (20X2)(10X1)=  50KNm
Problems on simply supported beams
1)
Step 1: Calculation of the reactions
ΣH = 0
ΣV = 0
Ra+ Rb= 4+10+7
Ra+ Rb= 21KN
ΣMa =0
Rb(8)7(6)10(4)4(1.5)=0
Rb = 11 KN ; Ra = 10 KN
Step 2: Calculation of shear force
Shear force at point B = 11KN
Shear force at point C= 11+ 7= 4KN
Shear force at point D=11+ 7+10 = 6KN
Shear force at point E= 11+ 7+10+4 = 10KN
Shear force at point A=10KN
Step 3: Calculation of Bending Moment
Bending Moment at point B= 0KNm
Bending Moment at point C= (11X2)= 22KNm
Bending Moment at point D= (11X4)(7X2)=30KNm
Bending Moment at point E= (11X6.5)(7X4.5)(10X2.5)= 15KNm
Bending Moment at fixed point A=(11X8)(7X6)(10X4)(4X1.5) = 0KNm
Step 1: Calculation of the reactions
ΣH = 0
ΣV = 0
Ra+ Rb= 2+5+4
Ra+ Rb= 11KN
ΣMa =0
Rb(6)4(4.5)5(3)2(1.5)=0
Rb = 6 KN ; Ra = 5 KN
Step 2: Calculation of shear force
Step 2: Calculation of shear force
Shear force at point B = 6KN
Shear force at point E= 6+4= 2KN
Shear force at point D=6+ 4+5 = 3KN
Shear force at point C= 6+ 4+5+2 = 5KN
Shear force at point A=5KN
Step 3: Calculation of Bending Moment
Bending Moment at point B= 0KNm
Bending Moment at point E= (6X1.5)= 9KNm
Bending Moment at point D= (6X3)(4X1.5)=12KNm
Bending Moment at point C= (6X4.5)(4X3)(5X1.5)= 7.5KNm
Bending Moment at fixed point A=(6X6)(4X4.5)(5X3)(2X1.5) = 0KNm
3)
Step 1: Calculation of the reactions
ΣH = 0
ΣV = 0
Ra+ Rb= 3+6
Ra+ Rb= 9 KN
ΣMa =0
Rb(6)6(4)3(2)=0
Rb = 5KN ; Ra = 4 KN
Step 2: Calculation of shear force
Step 2: Calculation of shear force
Shear force at point B = 5KN
Shear force at point D= 5+6= 1KN
Shear force at point C= 5+6+3 = 4KN
Shear force at point A= 4KN
Step 3: Calculation of Bending Moment
Bending Moment at point B= 0KNm
Bending Moment at point D= (5X2)= 10KNm
Bending Moment at point C= (5X4)(6X2)=8KNm
Bending Moment at fixed point A=(5X6)(6X4)(3X2) = 0KNm
4)
Step 1: Calculation of the reactions
ΣH = 0
ΣV = 0
Ra+ Rb= 10(6)
Ra+ Rb= 60 KN
ΣMa =0
Rb(12)10(6)(3)=0
Rb = 15KN ; Ra = 45 KN
5)
Step 2: Calculation of shear force
Shear force at point B = 15KN
Shear force at point C= 15KN
Shear force at point A= 15+10(6)= 45 KN
Step 3: Calculation of Bending Moment
Bending Moment at point B= 0KNm
Bending Moment at point C= (15X6)=90KNm
Bending Moment at fixed point A=(15X12)(10X6X3)= 0KNm
5)
Step 1: Calculation of the reactions
ΣH = 0
ΣV = 0
Ra+ Rb= 5(2)+ 10(2)
Ra+ Rb= 30 KN
ΣMa =0
Rb(6)5(2)(4+1)10(2)1=0
Rb = 11.67KN ; Ra = 18.33 KN
Step 2: Calculation of shear force
6)
Step 2: Calculation of shear force
Shear force at point B = 11.67KN
Shear force at point D= 11.67+5X2= 1.67KN
Shear force at point C= 1.67 KN
Shear force at point A= 1.67+ 10X2 = 18.33KN
Step 3: Calculation of Bending Moment
Bending Moment at point B= 0KNm
Bending Moment at point D= (11.67X2)(5X2X1)= 13.34KNm
Bending Moment at point C= (11.67X4)(5X2)(1+2)=16.68KNm
Bending Moment at fixed point A=(11.67X6)(5X2)(1+4)(10X2X1) = 0 KNm
Step 4: Calculation of point of zero shear force x(point of max BM)
Ra10(x)=0
18.3310(x)=0
x=1.833m
Maximum BM corresponding to x
Ra(x)10(x2/2)
18.33(1.833)10(1.833x1.833/2)
16.79KNm = Mmax
6)
Step 1: Calculation of the reactions
ΣH = 0
ΣV = 0
Ra+ Rb= 50+ 10(4)+40
Ra+ Rb= 130 KN
ΣMa =0
Rb(10)40(6)10(4)(2+2)50x2=0
Rb = 50 KN ; Ra = 80 KN
Step 2: Calculation of shear force
Step 2: Calculation of shear force
Shear force at point B = 50KN
Shear force at point D= 50+40= 10KN
Shear force at point C= 50+40+10x4+50= 80 KN
Shear force at point A = 80 KN
Step 3: Calculation of Bending Moment
Bending Moment at point B= 0KNm
Bending Moment at point D= (50X4)= 200 KNm
Bending Moment at point C= (50X8)(40X4)(10x4x2)=160 KNm
Bending Moment at fixed point A = 0 KNm
Step 4: Calculation of point of zero shear force x(point of max BM)
Ra5010(x2)=0
805010(x2)=0
x=5 m
Maximum BM corresponding to x
Ra(x)50x310x3x1.5
205 KNm = Mmax
7)
8)
7)
Step 1: Calculation of the reactions
ΣH = 0
ΣV = 0
Ra+ Rb= 4+ 8+8
Ra+ Rb= 20 KN
ΣMa =0
Rb(10)8(9)8(5)4(2)=0
Rb = 12 KN ; Ra = 8 KN
Step 2: Calculation of shear force
Step 2: Calculation of shear force
Shear force at point B = 12 KN
Shear force at point F= 12+8= 4 KN
Shear force at point E= 4 KN
Shear force at point D= 4+8= 4 KN
Shear force at point C= 4+4= 8 KN
Shear force at point A = 8 KN
Step 3: Calculation of Bending Moment
Bending Moment at point B= 0KNm
Bending Moment at point F= (12X1)= 12 KNm
Bending Moment at point E= (12X3)(8x2)=20 KNm
Bending Moment at point D= (12X7)(8x6)(8x2)=20 KNm
Bending Moment at point C= (12X8)(8x7)(8x3)(4x2)=8 KNm
Bending Moment at fixed point A = 0 KNm
Step 4: Calculation of point of zero shear force x(point of max BM)
Ra42(x3)=0
842(x3)=0
x=5 m
Maximum BM corresponding to x
Ra(x)4x34x1
24 KNm = Mmax
8)
Step 1: Calculation of the reactions
ΣH = 0
ΣV = 0
Ra+ Rb= 25+ 10(6)
Ra+ Rb= 85 KN
ΣMa =0
Rb(6)25(2)10(6)(6/2)=0
Rb = 38.33 KN ; Ra = 46.67 KN
Step 2: Calculation of shear force
Shear force at point B = 38.33 KN
Shear force at point C=38.33+10(4)+25= 26.67 KN
Shear force at point A =38.33+10(6)+25 =46.67 KN
Step 3: Calculation of Bending Moment
Bending Moment at point B= 0KNm
Bending Moment at point C= (38.33X4)(10x4x2)(25x2)=73.33 KNm
Bending Moment at fixed point A = 0 KNm
Step 4: Calculation of point of zero shear force x(point of max BM)
Ra2510(x)=0
46.672510(x)=0
x=2.167 m
Maximum BM corresponding to x
Ra(x)25x0.16710x2.167x2.167/2
73.48 KNm = Mmax
Step 1: Calculation of the reactions
ΣH = 0
ΣV = 0
Ra+ Rb= 0
Ra = Rb
ΣMa =0
Rb(6)24=0
Rb = 4 KN ; Ra = 4KN
Step 2: Calculation of shear force
Step 2: Calculation of shear force
Shear force at point B = 4 KN
Shear force at point C= 4 KN
Shear force at point A =4 KN
Step 3: Calculation of Bending Moment
Bending Moment at point B= 0KNm
Bending Moment at point C = Right side of C=4(4)= 16 KNm
= Left side of C = 4(2) = 8 KNm
Bending Moment at fixed point A = 0 KNm
Step 1: Calculation of the reactions
ΣH = 0
ΣV = 0
Ra+ Rb= 45+ 10(3)
Ra+ Rb= 75 KN
ΣMa =0
Rb(6)45(3)10(3)(3/2)120=0
Rb = 50 KN ; Ra = 25 KN
Step 2: Calculation of shear force
Shear force at point B = 50 KN
Shear force at point D=50 KN
Shear force at point C=50+45 = 5 KN
Shear force at point A =5+10(3) =25KN
Step 3: Calculation of Bending Moment
Bending Moment at point B= 0KNm
Bending Moment at point D= from B = 50x1.5120= 45 KNm
Bending Moment at point C = 50x3120 =30 KNm
Bending Moment at fixed point A = 0 KNm
Step 4: Calculation of point of zero shear force x(point of max BM)
Ra10(x)=0
2510(x)=0
x=2.5 m
Maximum BM corresponding to x
Ra(x)10x2.5x2.5/2
31.25 KNm = Mmax
Step 1: Calculation of the reactions
ΣH = 0
ΣV = 0
Ra+ Rb= 40+ 5(2)
Ra+ Rb= 50 KN
ΣMa =0
Rb(7)40(2)5(2)((2/2)+2))80=0
Rb = 27.14 KN ; Ra = 22.86 KN
Step 2: Calculation of shear force
Shear force at point B = 27.14 KN
Shear force at point C = 27.14 KN
Shear force at point D= 27.14 KN
Shear force at point E= 27.14+5(2)+40 = 22.86 KN
Shear force at point A = 22.86 KN
Step 3: Calculation of Bending Moment
Bending Moment at point B= 0KNm
Bending Moment at point C =27.14x180=52.86 KNm
Bending Moment at point D =27.14x380=1.42 KNm
Bending Moment at point E = 27.14x5805(2)(2/2)=50.7 KNm
Bending Moment at fixed point A = 0 KNm
Step 1: Calculation of the reactions
ΣH = 0
Ha = 100cos60+200cos45+300cos30
Ha = 451.23KN
Ha = 100cos60+200cos45+300cos30
Ha = 451.23KN
ΣV = 0
Ra+ Rb= 100sin60+200sin45+300sin30
Ra+ Rb= 378KN
ΣMa =0
Rb(4)300(3sin30)200(2)(sin45)100sin60=0
Rb = 204.86 KN ; Ra = 173.14KN
Step 2: Calculation of shear force
Shear force at point B = 204.86 KN
Shear force at point E= 204.86+300sin30= 54.86 KN
Shear force at point D= 204.86+300sin30+200sin45= 86.56KN
Shear force at point C= 204.86+300sin30+200sin45+100sin60 = 173.14 KN
Shear force at point A =173.14KN
Step 3: Calculation of Bending Moment
Bending Moment at point B= 0KNm
Bending Moment at point E=204.86x1= 204.86 KNm
Bending Moment at point D =204.86x2300sin30 =259.72 KNm
Bending Moment at point C =204.86x3300(2)sin30200(2)sin45=126.84 KNm
Bending Moment at fixed point A = 0 KNm
Step 1: Calculation of the reactions
ΣH = 0
ΣV = 0
ΣV = 0
Ra+ Rb= 0.5(5)(6)
Ra+ Rb= 15KN
ΣMa =0
Rb(5)0.5(5)(6)(1/3)(5)=0
Rb = 5 KN ; Ra = 10KN
Step 2: Calculation of shear force
ΣMa =0
Step 2: Calculation of shear force
Shear force at point B = 5 KN
Shear force at point B = 10 KN
Step 3: Calculation of Bending Moment
Bending Moment at point B= 0KNm
Bending Moment at point A= 0KNm
Step 4: Calculation of point of zero bending moment
Rb + (0.5)(x)(6x/5) = 0
x = 2.88m
Maximum bending moment = Rb(x)  (0.5)(x)(6x/5)(x/3)
Mmax = 9.62KNm
Step 1: Calculation of the reactions
ΣH = 0
ΣV = 0
Ra+ Rb= 30+ 0.5(3)(20)
Ra+ Rb= 60KN
ΣMa =0
Rb(6)30(5)0.5(3)(20)(1+(2/3(3))=0
Rb = 40KN ; Ra = 20 KN
Step 2: Calculation of shear force
Shear force at point B = 40 KN
Shear force at point E = 40+30 = 10 KN
Shear force at point D= 10 KN
Shear force at point C= 10+(0.5)(3)(20)= 20 KN
Shear force at point A = 20 KN
Step 3: Calculation of Bending Moment
Bending Moment at point B= 0KNm
Bending Moment at point E= 40X1=40 KNm
Bending Moment at point D =40x230x1=50KNm
Bending Moment at point C = 40x530x40.5(20)(3)(2/3(3))=20KNm
Bending Moment at fixed point A = 0 KNm
Step 4: Calculation of point of zero bending moment
Ra  (0.5)(x1)(20/3)(x1) = 0
x = 1.45m
Maximum bending moment = Ra(x)  (0.5)(x1)(20/3)(x1)(2/3)(x1)
Mmax = 28.79KNm
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