draw the shear force and bending moment diagram for the beam of span 10m long shown in the fig
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Step-by-step explanation:
Can you draw the shear force and bending moment diagrams of the beam shown in the figure below considering the given load?
https://i.hizliresim.com/gFv7qV.jpg
12 Answers

Roy Narten, Mechanical Engineer - I taught this stuff
Answered 7 months ago · Author has 1.3K answers and 2M answer views
EDIT 2020–09–14

Without explaining all the calculus to prove it, a simple rule of thumb is:
the change in shear = -(area under the load curve (w))
slope of the V curve = -(w)
slope of the M curve = V
the change in M = area under the V curve.
Here’s how I got my numbers:
First calculate the reactions at the support as I’ve shown on the diagram.
Between A and B:
The 25 kN load “pushes” the shear diagram down by 25. There is no load (or “w”) between A and B so the slope of the V-curve =0 between A and B. i.e. no change in V.
No M at the end of the beam so begin drawing M diagram at zero. Between A and B, slope of M=V, so slope=-25 i.e. a straight line.
Between B and C:
The load is zero at B and increases linearly to 30 at C.
Since the slope of V = -w, slope of V is zero at B and slope increases to -30 at C forming a parabolic curve.
Since the slope of M = V, slope of M is -25 at B and slope increases to -70 at C forming a cubic curve.
Note that the change in shear between B and C = area under the load curve (I called A1). So -25 - 45 = -70 kN.
Note that the 70 kN reaction force at the support will return the shear force diagram from -70 kN back to zero.
Between C and D:
No loading, so the shear diagram doesn’t change. i.e. a horizontal line still at -70.
Since the slope of V = -w, slope of M is zero, verifying that it is a horizontal line.
Since the slope of M = V, slope of M is -70 at C and is constant slope to D (straight line).
To get the magnitude of the bending moment at C, I simply took the maximum moment (at D) of 285 and subtracted the area under the shear diagram (area A3) between C and D. 285–140–145.
EDIT: Let’s assume you didn’t calculate the reactions at the support. To get the magnitude of the bending moment at each point, simply calculate the area’s under the shear force diagram as follows: Starting for the left side, area A2A2 = (25)(1)=25 kNm. this is the change in the moment diagram from point A to B. The change in the moment diagram from B to C equals the area above the x2x2 curve in the V-diagram = A4+A5A4+A5.
A4A4 = (3)(25)=75 kNm
and the formula for A5A5 is 13BH=13(3)(70−25)13BH=13(3)(70−25) = 45 kNm
So the total change in the bending moment from point A to B = A2+A4+A5A2+A4+A5 = 25+75+45 = 145 kNm. And finally, adding A3A3 =140 gives the moment at D. i.e. 145+140=285 kNm.
Step-by-step explanation:
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