Relation between intensity bending moment and shear force, Mechanical Engineering

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

 

Posted Date: 10/20/2012 1:25:46 AM | Location : United States







Related Discussions:- Relation between intensity bending moment and shear force, Assignment Help, Ask Question on Relation between intensity bending moment and shear force, Get Answer, Expert's Help, Relation between intensity bending moment and shear force Discussions

Write discussion on Relation between intensity bending moment and shear force
Your posts are moderated
Related Questions
Single Cylinder Vertical Engine has a bore of 30cm and a stroke of 40cm. The connecting rod is 100cm long. The mass of the reciprocating parts is 140Kg on the expansion stroke with

Explain the meaning of A raft foundation A raft foundation, as also combined footing, cannot be considered to be the opposite of a slab supported on the columns with a defined

(i) Formulate the equation of motion for the system shown in Figure. List TWO (2) assumptions made in this formulation. (ii) Find the response of this system at t = 3s. The syst

A cart is moving along a track at a constant velocity of 5 m/s as shown. Water (? = 1000 kg/m3) issues from a nozzle at 10 m/s and is deflected through 180° by a vane on the cart.

prove that the sensitiveness of a proell governor is greater than that of a porter governor

#tool life formular for diferent n values

Name The Boolean Set Operators used in CSG The Boolean Set Operators used are : union : A + B is the set of points that are in A or B. intersection : A . B is the s

Deflection at the centre: A simply supported beam of span 6 m is subjected to Udl of 24 kN/m for a length of 2 m from left support. Discover the deflection at the centre, maxi

Consider a fully developed laminar flow of a fluid through a 200 m long and 4 cm diameter horizontal and circular pipe. The density and the viscosity of the fluid are 1400 kg/m 3

ES 347 - Thermodynamics Project Assigned: 3/28/2013 Due: 4/25/2013 Problem specification 5 kg of air is contained in a piston-cylinder device, initially at a pressure of 2MPa and a