Bending Moment for Bending Diagram

[lee123456789]

Hi
Im a bit confused with the example
Can somebody explain and show to me how they got the bending moment calculations for the diagram in the attached. i understand it up to there.

I started course late and can't ask for help.
Thanks

 

[Lnewqban]

What is exactly what confuses you about these calculations?
What do you believe that you have missed from the course so far?

 

[lee123456789]

Bending Moment, i understand you times the 7.125 by various distance to find points along the bending moment digram. I don't get why after they subtracted various increments after.

e.g
6m
BM = (7.125 x 6) - (6x3.5) - (4x0.5)
or
7m
(7.125x7) - (6x5.5)-(4x2.5)

The course been running for 3 weeks and was late to enrolling and only just started looking at this in half term. so missed point loads, UDL, bending moment, Digrams and stuff.

 

[Lnewqban]

Bending Moment, i understand you times the 7.125 by various distance to find points along the bending moment digram. I don't get why after they subtracted various increments after.

e.g
6m
BM = (7.125 x 6) - (6x3.5) - (4x0.5)
or
7m
(7.125x7) - (6x5.5)-(4x2.5)

The course been running for 3 weeks and was late to enrolling and only just started looking at this in half term. so missed point loads, UDL, bending moment, Digrams and stuff.

Rather than calculating internal moments in the beam at each point onto which a punctual force is applied (normal way), this person has assigned different values of x starting from the left end.

The shown left to right summation for x=6 m is incorrect.
It should have been:
$M_{x=6~m}=[(4~KN)(6.0-4.5)]+[(6~KN)(6.0-1.5)]-[(7.125~KN)(6.0)]$

The shown left to right summation for x=7 m is incorrect.
It should have been:
$M_{x=7~m}=[(4~KN)(7.0-4.5)]+[(6~KN)(7.0-1.5)]-[(7.125~KN)(7.0)]$

Note that the signs for each moment has been reversed from normal convention.

Please, see:
https://en.m.wikipedia.org/wiki/Shear_and_moment_diagram

https://www.engineeringtoolbox.com/beam-stress-deflection-d_1312.html

https://mathalino.com/reviewer/mechanics-and-strength-of-materials/shear-and-moment-diagrams

https://mathalino.com/reviewer/mech...materials/chapter-4-shear-and-moment-in-beams

https://mathalino.com/reviewer/mech...erials/relation-between-load-shear-and-moment

https://www.eng-tips.com/viewthread.cfm?qid=407272

 

[Dr.D]

T he straight lines in the moment diagram you have drawn are not correct. Bending moment is the integral of the shear function, so shear must represent the slope of the moment diagram.