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
Forces working on sphere: Let a sphere of mass m, suspended by means of a string, resting against a smooth wall, as illustrated in Figure (a). What are the forces working on i

how to design and fabricate wilson hartnell governor?

Q. What do you mean by Risers and Downcomers? Risers and downcomers shall be staggered along the shell of the WHB and steam drum for uniform water/steam circulation in the syst

Space Time Structure If the position of the particle  P  changes, the differential change in its position vector r is, in general, given by, d r = d x  i + d y  j + d z  k

Q. What do you mean by Levelling Procedure? The Surveyor shall calculate required field adjustment in module elevation based on data from survey in conjunction with correspondi

Ask question Briefly explain how, using Newton’s Law of cooling, you may write the temperature of a cooling body as an exponential function of time#Minimum 100 words accepted#

Mounting Systems For The  Welding Head-Carriage mounted type In this set up, the welding head is mounted on a movable carriage. The carriage is mounted on rails and powered by a

Water flows into the sink shown in figure 5 at a flow rate of 8 L/min. If the drain is closed, the water will eventually flow through the overflow drain holes rather than over the

is it correct tosay tha the heat content of the system is 5 kv.

Q. Production Test Rings? The frequency for the tests shall be as follows: • One sample at the 10th joint • One sample at the 75th joint • One sample at the 300th join