Understanding Moment Diagrams: Why is the Maximum Moment at Point B?

[chetzread]

Homework Statement

http://www.mathalino.com/reviewer/m...tion-to-problem-403-shear-and-moment-diagrams

taking this as example , we notice that the moment varies linearly (from 0 to max from A to B ) (pls concentrate on part between A and B ) , why the moment is max at B (hinge) ? why shouldn't the moment at min at A ( location where the force act) ?

Homework Equations

The Attempt at a Solution

is it wrong ? i think the moment diagram should be drawn from moment (max ) to 0 at B , am i correct ? (red colour part which is drawn by me )

 

[SteamKing]

Homework Statement

http://www.mathalino.com/reviewer/m...tion-to-problem-403-shear-and-moment-diagrams

taking this as example , we notice that the moment varies linearly (from 0 to max from A to B ) (pls concentrate on part between A and B ) , why the moment is max at B (hinge) ? why shouldn't the moment at min at A ( location where the force act) ?

Homework Equations

The Attempt at a Solution

is it wrong ? i think the moment diagram should be drawn from moment (max ) to 0 at B , am i correct ? (red colour part which is drawn by me )

The bending moment is zero at point A and -30 kN-m at point B. How could it be otherwise?

Remember, M = F × d, and if d = 0, then M = 0.

At point A, the distance to the force F is d = 0, therefore M must be zero at A.

 

[pongo38]

I think the confusion might be that the hinge at B is drawn to hide the fact that the beam is moment-continuous over it. Thinking of the beam as a continuous, some rotation can occur there, but not the complete rotation as in a mechanism, that I suspect the op is thinking about.

 

[chetzread]

I think the confusion might be that the hinge at B is drawn to hide the fact that the beam is moment-continuous over it. Thinking of the beam as a continuous, some rotation can occur there, but not the complete rotation as in a mechanism, that I suspect the op is thinking about.

Thanks for ur reply !
now , my problem is the shear force act 26N downwards at point B...how can there still gt momenit about point B ? or the moment graph (from -30Nm to 0 ) is moment about other point (not B )?

 

[SteamKing]

I think the confusion might be that the hinge at B is drawn to hide the fact that the beam is moment-continuous over it. Thinking of the beam as a continuous, some rotation can occur there, but not the complete rotation as in a mechanism, that I suspect the op is thinking about.

I think this beam has two pinned connections, one at B and the other at D. I prefer to call them pinned connections, rather than hinges, since the latter term is often used in a slightly different context with beam problems.

The OP seems hazy on the fact that the area under the shear force curve leads to the ordinates of the bending moment curve. Since the beam is free at the extreme left end, the shear force there is the 30 kN as shown on the diagram, but the moment is 30 kN ⋅ dx, where dx is the distance measured from the left end of the beam. Obviously, when dx = 0, then M = 0, not M = 30 kN-m.

 

[SteamKing]

Thanks for ur reply !
now , my problem is the shear force act 26N downwards at point B...how can there still gt momenit about point B ? or the moment graph (from -30Nm to 0 ) is moment about other point (not B )?

It's not clear what you are trying to say here.

You have a downward shear force of 30 kN which is applied at the extreme left end of this beam. This shear force remains constant until you reach the support at B, where there is an upward reaction of 56 kN. V = +56 kN - 30 kN = +26 kN after point B, which is the value shown on the shear force diagram. This shear force remains constant until you reach point C, where another 50 kN load is applied pointing down. V = +26 kN - 50 kN = -24 kN after point C. Again, this shear force value remains constant until the support at D is reached, where the reaction is RD = +24 kN. The shear force after point D is then V = -24 kN + 24 kN = 0, which indicates that the beam is in equilibrium as far as the forces acting on it are concerned.

With regards to the bending moment.your mistake was to assume that the moment due to the -30 kN load taken about point B occurs at the location of the load. This is simply not true. A moment is the product of a force and a distance. The -30 kN force wants to rotate the end of the beam about point B, not anywhere else. Therefore, the moment M = -30 kN-m is plotted at point B and not the left end of the beam.

Once you understand this, then constructing the moment curve from the shear curve should follow very easily.