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

Camshaft-basic components of engine , Camshaft : The camshaft controls th...

Camshaft : The camshaft controls the opening and closing of the two valves. The associated parts are push rods, rocker arms and valve springs. The camshaft is driven by a camchai

Define application of electro discharge machining, Normal 0 fal...

Normal 0 false false false EN-IN X-NONE X-NONE MicrosoftInternetExplorer4

ESSENTIALS OF PROJECT MANAGEMENT, Ask qu1. A small maintenance project cons...

Ask qu1. A small maintenance project consists of the following 10 jobs, whose precedence relationships are identified by their node numbers: JOB NODE NUMBERS ESTIMATED DURATION (DA

Determine reactions force, Determine reactions force: Thr e e spher...

Determine reactions force: Thr e e sphere A , B and C weighing 400N, and 200N and having radii 400mm,  600mm and 400mm respectively are placed in trench as shown in t

Design temporary storage, Q. Design Temporary Storage? It is sometimes ...

Q. Design Temporary Storage? It is sometimes acceptable to store drums temporarily on spill containment pallets. Each pallet should be capable of capturing the contents of at l

Key words used in road under special conditions, Keywords used in appropria...

Keywords used in appropriate technology: Hill Roads : Roads in hilly and mountainous terrain. Landslides : The slippage of mass of hill face. Retaining Walls : Str

Load shared by concentric springs, Load shared by concentric springs: ...

Load shared by concentric springs: Two concentric springs are subjected to an axial load of 60 kN. The maximum permissible deflection of the springs is 45 mm & the solid lengt

Gmaw power source, GMAW POWER SOURCE A power source wit h a flat charac...

GMAW POWER SOURCE A power source wit h a flat characteristics is almost universally used for GMAW process as it provides self adjustment and stabilisation of the arc. Also it m

Compute the angular velocity of the wheel, Compute the angular velocity of ...

Compute the angular velocity of the wheel: A wheel of 0.5 m radius rolls over a horizontal surface without slipping as illustrated in Figure (a). The velocity of its centre is

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