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isn't the bending moment supposed to be zero on roller supports at beams? then why isn't it zero here in this picture at x=2? Bending moment at x=2 is not zero!

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no. The change in moment is zero, as you can see on your plot.

I think you can see if you imagine sectioning the beam slightly to the right of the support and constructing a free body diagram, the moment there is not zero. the support does not provide any concentrated moment, so the moment does not change there and so the moment at the support can not be zero.

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  • $\begingroup$ Strictly speaking (for a dimensionless roller), isn't the derivative undefined, rather than zero? $\endgroup$ – Carl Witthoft Jan 11 '18 at 15:38
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    $\begingroup$ @CarlWitthoft right. The curve is continuous but not differentiable. $\endgroup$ – agentp Jan 11 '18 at 15:53
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Bending moment is the area under the shear diagram which is definitely increasing by a slope of 5kn/m as it gets closer to support in a straight line, so it is maximum on the support. And this moment is balanced by the reaction of roller.

If you remove the continuity in beam over the roller and allow a joint there thus removing the moment there, the cantilever part will immediately lose its equlibrium and rotate clockwise down and will turn into a pendelum swinging back and forth!

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Moment in gerber joint or hinge equals zero, but moment in roller support is not necessarily zero. Moment is double integral of beam load. Reaction force in roller support causes sudden change of moment curve tangent slope.

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