Numerical problems based on the cantilever beam, Mechanical Engineering

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

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

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

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

2195_Numerical Problems Based on the Cantilever Beam3.png 

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

 

Posted Date: 10/20/2012 1:49:47 AM | Location : United States







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