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
The rigidly jointed frame shown in Figure has bending stiffnesses such that EI AB = 1000kNm 2 and EI BC = EICD = 1600kNm 2 . (i) Determine the joint rotations at B and C.

ELECTRON BEAM WELDING PROCESS AND ITS APPLICATIONS   Electron Beam Welding (EBW) is one of the advanced welding technologies required for the precision welding applications

Q. Flange Assembly with Bolt Tensioning? Measure the free length of the bolts ultrasonically. This must be done prior to applying any load to the bolt. Install bolts on the

Question 1: There are different devices which may be used to attract the attention of the customers and persuade them to purchase merchandise. a) Make a list of at least te

Can you give me the Prove of the bending Equation M/I=E/R=σ/Y

what are the anti refection coating.expretion for thicknessrefractive index of coating material to act as anti reflacting coating

Laser-induced breakdown spectroscopy (LIBS) is a type of spectroscopy that uses plasma generated by a laser pulse. A schematic of a LIBS system is shown in the figure. The laser is

Q. Can you explain the Mobile bed model? Mobile bed models can again be either geometrically similar or vertically exaggerated. Models of the former type permit study of proble

Objectives After studying this unit, you should be able to discuss the scope and extent of service industry, describe the phases of two wheeler industry growth, an

Resultant of Non coplanar concurrent force system: How do you find resultant of Non coplanar concurrent force system? Sol.: The resultant of non concurrent force system