Relation between intensity bending moment and shear force, Mechanical Engineering

Assignment Help:

Relation between intensity bending moment and shear force:

What is the relation between load intensity bending moment and shear force

Consider the beam subjected to any type of transverse load of the general form shown in the figure given below. Isolate from the beam an element of length dx at a distance x from left end and draw its free body diagram as shown in the figure given below. As the element is of very small length, the loading over the beam is considered to be uniform and equal to w KN/m. The element is dependent on shear force F on the left hand side of it. Further bending moment M acts on left side of element and it changes to (M + dM) on right side.

 

1979_Relation between intensity bending moment and shear force.png

Taking moment about the point C on right side, ΣMC = 0

M - (M + dM) + F X dx - (W X dx) X dx/2 = 0

The UDL is considered to be acting at the Center of gravity
 dM = Fdx - [W(dx)2]/2 = 0

The last term comprises of the product of the two differentials and can be neglected

DM = Fdx, or

F = dM/dx

Therefore the Shear Force is equal to rate of change of bending moment with respect to x. Apply conditionΣV = 0 for equilibrium, we obtain

F - Wdx - (F + dF) = 0

Or                              W = dF/dx

That is intensity of loading is equal to rate of change of bending moment with respect to x.

F = dM/dx

and                           W = dF/dx = dM2/dx2

 


Related Discussions:- Relation between intensity bending moment and shear force

Explain working of steam drum, Q.Explain working of Steam Drum? Total so...

Q.Explain working of Steam Drum? Total solids concentration in the steam at steam manifold outlet shall not exceed 0.5 ppm during steady operation at MCR.  Fabricator must indic

Diaphragm spring single plate, Give the working and consideration of a diap...

Give the working and consideration of a diaphragm spring single plate clutch in disengaged position. Discuss in detail the constructional features of a clutch plate. Explain the

Find out the velocity of the chain, Find out the velocity of the chain: ...

Find out the velocity of the chain: Figure shows a metal chain ABC where portion BC is of length 0.4 metres and is hanging vertically, & portion AB of length 0.8 metres rests

Find out the reactions at point, Find out the reactions at point: A be...

Find out the reactions at point: A beam AB is hinged at A and is supported at C. It is loaded as revealed in Figure. Find out the reactions at A and C. Solution L

Hydraulic systems analysis, 1. A hydraulic pump generates 240W and supplies...

1. A hydraulic pump generates 240W and supplies hydraulic fluid at a rate of 5.1l/min to a linear actuator which has a bore size of 50 mm and a double piston rod diameter of 20mm.

Determine net work done, Determine net work done: 5 m 3   of air ...

Determine net work done: 5 m 3   of air at 2bar, 27 0 C is compressed to 6bar pressure following PV 1. 3   = constant. It is expanded subsequently adiabaticall

Explain degree of freedom - jig and fixture, Explain Degree of Freedom - Ji...

Explain Degree of Freedom - Jig and Fixture The complete location of components inside a jig or fixtures can be understood with the help of figure. The work piece is a

Robotic and manufacturing automation, Consider the robotic manipulator of F...

Consider the robotic manipulator of Fig. 1, with a Revolute and a Prismatic Joint. Figure 1, shows the side view of the manipulator while figure 2. shows the top view of the manipu

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd