1. Welcome to Neath Port Talbot College!

2. Point loads
The figure below illustrates a simply supported beam with a cantilever. The beam has two point loadings of 45kN and 24kN.
We shall calculate the value of the reactions. Before undertaking this calculation, we need to recap some of the basic laws associated with this type of structure;
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3. Conditions for Equilibrium
The sum of the forces in one direction must equal the sum of the forces in the opposite direction ie the sum of downward forces equals the sum of the upward forces.
Anti-clockwise moments equal clockwise moments
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4. Point Loads Moment about a point (pivot)
Moment = Force x Distance about a point
Force
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Distance

5. Point Loads Moment about a point This gives a CLOCKWISE MOMENT Pivot
Force (F)
MOMENT = F x D
Distance (D)
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6. Worked example 45KN 20KN 2m 3M 5M RR RL
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7. Worked example Calculate the left and right reactions
Take the left-hand reaction as the PIVOT:
Anti-clockwise moments = Clockwise moments
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8. Worked example Anti-clockwise moments = Clockwise moments
RR x 7 = (20 x 10) + (45 x 2)
RR x 7 = 290
RR = 290/7
= Kn
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Therefore RL = 65 – RR = Kn

9. Worked example RR = 41.43 Kn RL = 23.57 Kn Check
ΣUPWARD FORCES = ΣDOWNWARD FORCES
= 65 ( ) correct
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10. Worked example 20KN 45KN CWM CWM ACWM 2m 5M 3M RL RR
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Moments created by each force when considered individually

11. Deflected Shape This is the deflected shape (Exaggerated)
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This is the deflected shape (Exaggerated)

12. Shear Force Diagram
20.00
20.00
23.57
23.57
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-21.43
-21.43
SHEAR FORCE DIAGRAM

13. Bending Moment A C D B Find the BM values at points A, B, C & D
The BM value at the ends of a simply supported beam is always ZERO.
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In this case BMA & BMD equal 0 Knm

14. Bending Moment A C D B Find the BM values at points B & C
Consider all loads to the left of the point where a BM value is required.
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15. Bending Moment A C D B BM value at points B. Consider the following:
BMB = +(23.57x 2) = Knm B 2m
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CLOCKWISE MOMENTS CONSIDERED TO BE POSITIVE.
23.57

16. Bending Moment A C D B
45Kn
BM value at points C. Consider the following:
BMC = +(23.57x7) – (45x5) = Knm C 2m 5m
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ANTI CLOCKWISE MOMENTS CONSIDERED TO BE NEGATIVE.
23.57Kn

17. Bending Moment Diag: A C D B Note! Positive values plotted BELOW
Negative values plotted ABOVE
60.01 B
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47.14

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