Simply supported beams Beams are used in engineering

Simply supported beams • Beams are used in engineering as support for loaded systems • Examples: • rectangular section and I-section beams that are used to support brickwork above windows and doors, • Rail tracks, Bridge decking supports beams etc.

A moment • Is simply a force that produces a turning effect. • When using a spanner to tighten a nut, a force tends to turn the nut in a clockwise direction. • This turning effect is called the moment of a force or just moment the moment M of a force acting about a point P is force x distance between the line of action of the force and P i. e. M=F×d Where M is the moment in Newtons-metres, F is the force in Newtons and d is the distance in metres.

Work example 1 A force of 15 N is applied to a spanner at an effective length of 140 mm from the centre of a nut. Calculate: a. The moment of the force applied to the nut, b. The magnitude of the force required to produce the same moment if the effective length is reduced to 100 mm. From the above, M = F X d, Turning moment, M = 15 N x 140 mm = 2100 N mm = 2100 N mm x 1 mm 1000 mm = 2. 1 N m • Turing moment, M is 2100 N mm and the effective length d becomes 100 mm (see fig 2 b) Applying M=Fxd gives : 2100 N mm = F x 100 mm from which force, F = 2100 N mm =21 N 100 mm

Time for short class exercise

Equilibrium and the principles of moments • A beam is said to be in equilibrium when there is no tendency for it to move • Conditions of static equilibrium: • Upwards forces = downwards forces • The sum of the CWM about any point = the sum of the ACWM at any point • The algebraic sum of the moments is equal to zero, that is ∑ CWM –∑AWM = 0 Rp = F 1 + F 2 What happens when one person moves closer to the fulcrum or pivot? Clearly, the see-saw will tip down at the green end. The reason for this is that the turning effect of the force is dependant on the distance of the force from the pivot

Work example A system of forces is as shown • If the system is in equilibrium find the distance d • If the point of application of 5 N force is moved to point P, distance 200 mm from the support, and the 5 N force is replaced by an unknown force F, find the value of F for the system to be in equilibrium.