Numerical Problems Based on the Cantilever Beam:
Draw the SF and BM diagram for the beam as shown in the figure given below. Also indicate principal values on diagrams.
![715_Numerical Problems Based on the Cantilever Beam.png](https://www.expertsmind.com/CMSImages/715_Numerical Problems Based on the Cantilever Beam.png)
Sol.: Let reaction at the support A be RAV, RAH and M(counter clock wise), First find support reaction
For that,
ΣV = 0
RAV -2 -3 -3 = 0, RAV = 8 ...(1)
Taking moment about A,
ΣMA = 0
-M + 2 X 1 + 3 X 3 + 3 X 5 = 0
M = 26KNm ...(2)
ΣH = 0
RAH = 0
![2301_Numerical Problems Based on the Cantilever Beam1.png](https://www.expertsmind.com/CMSImages/2301_Numerical Problems Based on the Cantilever Beam1.png)
Calculation for Shear force Diagram
Draw section line, here total 3 section line, which break the
load RAV and 2KN(in between A and B),
2KN and 3KN(Between B and C),
3KN and 3KN (Between C and D). Take left portion of the beam
Take section 1-1
Force on left of section 1-1 is RAV
SF1-1 = 8KN (constant value)
Constant value means that the value of shear force at both the nearest point of the section is equal that is
SFA = SFB = 8KN ...(4)
Take section 2-2
Forces on the left of section 2-2 is RAV and 2KN
SF2-2 = 8 - 2 = 6KN (constant value)
Constant value means that the value of shear force at both the nearest point of the section is equal that is
SFB = SFC = 6KN ...(5)
Take section 3-3
Forces on the left of section 3-3 is RA, 2KN, 3KN
SF3-3 = 8 - 2 - 3 = 3KN (having constant value)
Constant value means that the value of shear force at both the nearest point of the section is equal that is
SFC = SFD = 3KN ...(6)
Calculation for Bending moment Diagram
Assume
Distance of section 1-1 from A is X1
Distance of section 2-2 from A is X2
Distance of section 3-3 from A is X3
Take section 1-1, taking moment about the section 1-1
BM1-1 = 8.X1
It is Equation of straight line (Y = mX + C), inclined linear.
Inclined linear means that the value of bending moment at both the nearest point of section is varies with
![914_Numerical Problems Based on the Cantilever Beam2.png](https://www.expertsmind.com/CMSImages/914_Numerical Problems Based on the Cantilever Beam2.png)
It is Equation of the straight line (Y = mX + C), inclined linear.
Inclined linear means that the value of bending moment at both the nearest point of section varies with
That is inclined line 20 to 26
Plot the BMD with the help of obtained bending moment values. The SFD and BMD is shown in the figure