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

Illustrate clay content test, Q. Illustrate Clay content test? Under th...

Q. Illustrate Clay content test? Under this test, the clay content is measured by washing it off the sand sample. The standard dried sand sample (50 gm) is put in a mixing devi

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

Resistance welding electrodes and holders, Resistance welding electrodes an...

Resistance welding electrodes and holders Requisites For Electrodes : The resistance welding electrodes are meant for the following functions: Conducting electricity

Axial flow turbine, The mass flow rate is 28kg/s in an axial flow gas turbi...

The mass flow rate is 28kg/s in an axial flow gas turbine that develops 3.5MW. The stagnation conditions are 780KPa and 730 deg.C. at the entry. At the exit of the nozzle, the stat

Explain the side relief angle, Explain the Side Relief Angle It is angl...

Explain the Side Relief Angle It is angle made by flank of a tool and plane perpendicular to base just under the side cutting edge. if the side relief angle is very large the c

Mathematics, solve the following differential equation: dy/dx-(1+1/x)y=y^2

solve the following differential equation: dy/dx-(1+1/x)y=y^2

Stud welding, Stud Welding This is an arc welding process in which the...

Stud Welding This is an arc welding process in which the arc is struck between a metal stud or similar part and the base metal. The arc heats the mating ends to a proper tempe

Solve the equation by newton raphson method, Calculate root of equation 3x ...

Calculate root of equation 3x = 100 cosx + 1 by Newton Raphson method correct to three decimal places Calculate root of equation xe x = cosx by Secant method correct to three d

Determine the frictional resistance, Determine the frictional resistance: ...

Determine the frictional resistance:  (i) A train having weight 400 kN is running up an inclined path of 1 in 100 at a steady speed of 54 km/hour. If the frictional resistance

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