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







Related Discussions:- Numerical problems based on the cantilever beam, Assignment Help, Ask Question on Numerical problems based on the cantilever beam, Get Answer, Expert's Help, Numerical problems based on the cantilever beam Discussions

Write discussion on Numerical problems based on the cantilever beam
Your posts are moderated
Related Questions

Improvement Of Existing Airport: The improvements that are usually needed for existing airports fall under the following categories : (a)        Extension of runway to acco

Cross Drainage Works: Culverts A large number of culverts are needed for taking care of the streams crossing the railway lines. The culverts can be one of the followi

what is the meaning of translating roller follower and total follower travel?

Cope and drag pattern These are similar to split patterns. In addition to splitting the pattern, the cope and drag halves of the patterns along with the gating and risering sys

Working of Clutch : The clutches are operated mechanically through linkages. When operator presses the clutch lever, the pressure on the clutch plates reduces to zero, hence the c

Q. Scraper Launchers and Receivers? Scraper launchers and receivers associated with the pipelines shall be located in open, well-ventilated areas with the opening directed away

define elastomer.explain in details?

Characteristics of Adhesives and Adhesive Joints While an adhesive joint is created this has to show individual or several of given properties. (a) Mechanical strength again

Discover the maximum thickness required: A thin cylindrical vessel of 2 m diameter and 4 m length having a particular gas at a pressure of 1.65 N/mm 2 . If the allowable tensi