CONCURRENT FORCES & FORCE DIAGRAMS  A Concurrent Force System, is a force system where all forces start from the same point. 100N 200N  TERMS:  Resultant, the single force which can replace a force system.  Equilibrant, the single force which can bring a force system in to equilibrium.  To achieve equilibrium, all horizontal, vertical and moments must be balanced.  We can determine the value of the resultant and equilibrant through graphical techniques.

CONCURRENT FORCES & FORCE DIAGRAMS Lets consider the previous force system. 100N 200N 1.Select a scale to draw the forces against. In this case, lets say 5mm = 10N. 2.Draw the 200N force to scale, i.e. 100mm. 3.Draw the 100N force from the end of this vertically upwards. i.e. 50mm. 4. Join the ends and measure this line. 100mm 50mm Resultant Line length = Approx. 110mm So resultant = (110/5) x 10N = Approx. 220N

CONCURRENT FORCES & FORCE DIAGRAMS The Equlibrant will always be in the opposite direction, but will always have the same value. This technique works for force systems with more than 2 forces, as an example. F1 F2 F3 F4 Force System F1 F2 F3 F4 R

CONCURRENT FORCES & FORCE DIAGRAMS Pupil problems: N 30N 1)2) 50N 45 65N 3) 150N 50N 200N 75N

STRESS & STRAIN STRESS = Load/Cross Sectional Area (Nmm-2) Strain = Change in Length/ Original Length (no units) Example 1: A structural member is subjected to a compressive force of 20000N. If the diameter of the member is 250mm, calculate the stress within the member. If the load reduces the member length by 0.5mm and the original length was 2m, calculate the strain.

Solutions Strain Strain = Change in Length/ Original Length = 0.5/2000 =