Finding shearing force and moment

In summary: Because they are each integrals. The shear force is the integral of the load curve w.r.t. length, and the bending moment is the integral of the shear curve, also w.r.t. length.
  • #1
foo9008
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Homework Statement


i couldn't understand why the author take the distance of force 129kN for 4<x<6 and 6<x<8 is x-2 ?

Homework Equations

The Attempt at a Solution


IMO , for 4<x<6 , the distance of force 129kN to the point should be x , where x is the distance from the 129kN to the point of moment , correct me if i am wrong [/B]
 

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  • #2
is the author wrong ?
 
  • #3
The black dot on the left end of the x-axis is the origin (x=0), so the moment arm from x (the point about which the moment is being calculated) to the 192kN force is x-2.
 
  • #4
David Lewis said:
The black dot on the left end of the x-axis is the origin (x=0), so the moment arm from x (the point about which the moment is being calculated) to the 192kN force is x-2.
one more thing , why at x = 6 , the shearing force is still 49kN as in the calculation ? why shouldn't it be = 0 ?
 
  • #5
why at x = 2 , there are 2 values of shearing forces , namely -40kN (0<x<2) and 89kN (2<x<4) ?
 
  • #6
foo9008 said:
why at x = 2 , there are 2 values of shearing forces , namely -40kN (0<x<2) and 89kN (2<x<4) ?
Because the reaction RA is located at x = 2. As you move along the beam from left to right, the shear force has a sudden jump from V = -40 kN to V = 89 kN, as the reaction RA = 129 kN is added.
 
  • #7
foo9008 said:
one more thing , why at x = 6 , the shearing force is still 49kN as in the calculation ? why shouldn't it be = 0 ?
Why should the shear be zero at x = 6?

The shear force and the bending moment values are each cumulative starting at the left end of the beam. If there is no additional load applied to the beam, the shear force at a particular point will not be changed.
 
  • #8
SteamKing said:
Because the reaction RA is located at x = 2. As you move along the beam from left to right, the shear force has a sudden jump from V = -40 kN to V = 89 kN, as the reaction RA = 129 kN is added.
sudden jump means there are 2 values of RA at x =2 ? why ?
 
  • #9
can you explain why The shear force and the bending moment values are each cumulative starting at the left end of the beam.??
 
  • #10
foo9008 said:
can you explain why The shear force and the bending moment values are each cumulative starting at the left end of the beam.??
Because they are each integrals. The shear force is the integral of the load curve w.r.t. length, and the bending moment is the integral of the shear curve, also w.r.t. length.

The following slides explain this in more detail:

http://www.ce.memphis.edu/3121/notes/notes_04c.pdf
 
  • #11
foo9008 said:
sudden jump means there are 2 values of RA at x =2 ? why ?
No, there is only one value of RA, namely RA = 129 kN.

The shear force diagram is a plot of just the shear force values acting on the beam. When a concentrated load is encountered, such as one of the beam reactions or an applied load, the shear force diagram will show a jump discontinuity at that location. The size of the discontinuity = the magnitude on the concentrated force.
 
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  • #12
This is an example shear force and bending moment diagram for a simple beam. It is plotted in its entirety so that you can look at the entire diagram at once, and not a series of confusing snippets:


fig52bsfbm.gif

 

Related to Finding shearing force and moment

What is shearing force?

Shearing force is the force that acts parallel to the cross-sectional area of a material, causing it to deform or break. It is also known as transverse force.

How do you calculate shearing force?

Shearing force can be calculated by taking the sum of all the forces acting perpendicular to the cross-sectional area at a specific point. It is represented by the symbol "V" and is measured in Newtons (N) or pounds (lbs).

What is the difference between shearing force and bending moment?

Shearing force and bending moment are both forces that act on a material, but they have different effects. Shearing force causes a material to deform or break, while bending moment causes a material to bend or twist.

Why is it important to find shearing force and moment?

Knowing the shearing force and moment is crucial in understanding how a material will behave under different loads and stresses. This information is important in designing structures and machines that can withstand these forces without failing.

What are some common methods for finding shearing force and moment?

There are several methods for finding shearing force and moment, including graphical methods, analytical methods such as the shear and moment diagrams, and numerical methods such as the finite element method. The method used will depend on the complexity of the structure and the accuracy required.

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