Finding shearing force and moment

[foo9008]

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]

 

[foo9008]

is the author wrong ?

 

[David Lewis]

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.

 

[foo9008]

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 ?

 

[foo9008]

why at x = 2 , there are 2 values of shearing forces , namely -40kN (0<x<2) and 89kN (2<x<4) ?

 

[SteamKing]

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.

 

[SteamKing]

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.

 

[foo9008]

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 ?

 

[foo9008]

can you explain why The shear force and the bending moment values are each cumulative starting at the left end of the beam.??

 

[SteamKing]

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

 

[SteamKing]

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.

 

[SteamKing]

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:

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