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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; Names of who is presenting and positions What we are here to do today NB: you can also copy and use this slide as a template for further slides required with writing

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 Names of who is presenting and positions What we are here to do today NB: you can also copy and use this slide as a template for further slides required with writing

Point Loads Moment about a point (pivot) Moment = Force x Distance about a point Force Names of who is presenting and positions What we are here to do today NB: you can also copy and use this slide as a template for further slides required with writing Distance

Point Loads Moment about a point This gives a CLOCKWISE MOMENT Pivot Force (F) MOMENT = F x D Distance (D) Names of who is presenting and positions What we are here to do today NB: you can also copy and use this slide as a template for further slides required with writing

Worked example 45KN 20KN 2m 3M 5M RR RL Names of who is presenting and positions What we are here to do today NB: you can also copy and use this slide as a template for further slides required with writing RR RL

Worked example Calculate the left and right reactions Take the left-hand reaction as the PIVOT: Anti-clockwise moments = Clockwise moments Names of who is presenting and positions What we are here to do today NB: you can also copy and use this slide as a template for further slides required with writing

Worked example Anti-clockwise moments = Clockwise moments RR x 7 = (20 x 10) + (45 x 2) RR x 7 = 290 RR = 290/7 = 41.43 Kn Names of who is presenting and positions What we are here to do today NB: you can also copy and use this slide as a template for further slides required with writing Therefore RL = 65 – RR = 23.57 Kn

Worked example RR = 41.43 Kn RL = 23.57 Kn Check ΣUPWARD FORCES = ΣDOWNWARD FORCES 41.43 + 23.57 = 65 (45 + 20) correct Names of who is presenting and positions What we are here to do today NB: you can also copy and use this slide as a template for further slides required with writing

Worked example 20KN 45KN CWM CWM ACWM 2m 5M 3M RL RR Names of who is presenting and positions What we are here to do today NB: you can also copy and use this slide as a template for further slides required with writing RL RR Moments created by each force when considered individually

Deflected Shape This is the deflected shape (Exaggerated) Names of who is presenting and positions What we are here to do today NB: you can also copy and use this slide as a template for further slides required with writing This is the deflected shape (Exaggerated)

Shear Force Diagram 20.00 20.00 23.57 23.57 Names of who is presenting and positions What we are here to do today NB: you can also copy and use this slide as a template for further slides required with writing -21.43 -21.43 SHEAR FORCE DIAGRAM

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. Names of who is presenting and positions What we are here to do today NB: you can also copy and use this slide as a template for further slides required with writing In this case BMA & BMD equal 0 Knm

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. Names of who is presenting and positions What we are here to do today NB: you can also copy and use this slide as a template for further slides required with writing

Bending Moment A C D B BM value at points B. Consider the following: BMB = +(23.57x 2) = +47.14 Knm B 2m Names of who is presenting and positions What we are here to do today NB: you can also copy and use this slide as a template for further slides required with writing CLOCKWISE MOMENTS CONSIDERED TO BE POSITIVE. 23.57

Bending Moment A C D B 45Kn BM value at points C. Consider the following: BMC = +(23.57x7) – (45x5) = - 60.01Knm C 2m 5m Names of who is presenting and positions What we are here to do today NB: you can also copy and use this slide as a template for further slides required with writing ANTI CLOCKWISE MOMENTS CONSIDERED TO BE NEGATIVE. 23.57Kn

Bending Moment Diag: A C D B Note! Positive values plotted BELOW Negative values plotted ABOVE 60.01 B Names of who is presenting and positions What we are here to do today NB: you can also copy and use this slide as a template for further slides required with writing C 47.14

title content Names of who is presenting and positions What we are here to do today NB: you can also copy and use this slide as a template for further slides required with writing

title content Names of who is presenting and positions What we are here to do today NB: you can also copy and use this slide as a template for further slides required with writing

title content Names of who is presenting and positions What we are here to do today NB: you can also copy and use this slide as a template for further slides required with writing

title content Names of who is presenting and positions What we are here to do today NB: you can also copy and use this slide as a template for further slides required with writing

title content Names of who is presenting and positions What we are here to do today NB: you can also copy and use this slide as a template for further slides required with writing

title content Names of who is presenting and positions What we are here to do today NB: you can also copy and use this slide as a template for further slides required with writing

title content Names of who is presenting and positions What we are here to do today NB: you can also copy and use this slide as a template for further slides required with writing

title content Names of who is presenting and positions What we are here to do today NB: you can also copy and use this slide as a template for further slides required with writing

title content Names of who is presenting and positions What we are here to do today NB: you can also copy and use this slide as a template for further slides required with writing

title content Names of who is presenting and positions What we are here to do today NB: you can also copy and use this slide as a template for further slides required with writing