structures vary from the mundane

To the iconic

And entertaining

Natural structures can be even more amazing

Forces In this course we will deal with several forces acting on objects at one time Because forces have magnitude(size) and direction(angle) they are vectors.

See-saw In this see- saw how many forces are acting on the beam?

F1 F2 FRFR F 1 +F 2 = FRFR For static equilibrium the sum of the vertical forces must also = 0, F1F1 F2F2 FRFR

For static equilibrium the sum of the horizontal forces must also = 0,

Moments As well as the sum of vertical and horizontal forces on a body, the moments(or turning effect) of forces must also be zero for equilibrium

Moments If the sum of the moments(or turning effect) of forces are not zero you don’t have equilibrium lll4GF5g lll4GF5g

Moments

Now try assignments on moments of forces

Moments Conditions of Equilibrium In the force system in this section you shall apply the three condition of equilibrium that you have used in the following order 1. The sum of all the moments = zero. ∑M o = 0 2. The sum of all the vertical forces = zero. ∑ F v = 0 2. The sum of all the horizontal forces = zero. ∑ F h = 0

Moments A simply supported beam has no horizontal forces on it

Moments A simply supported beam has no horizontal forces on it We have to find R A and R B, the reaction forces supplied by the supports

Moments We have to find R A and R B, the reaction forces supplied by the supports

Moments We have to find R A and R B, the reaction forces supplied by the supports

Moments We have to find R A and R B, the reaction forces supplied by the supports

There are no horizontal forces in this simply supported beam ∑F h =0 So we just need to consider the vertical equilibrium 0.88kN ∑ F v = 0 R A + R B = R A = 17.12kN R A =18 – 0.88 R A = 18 R A = 17.12kN

Forces sometimes act at an angle so we need to be able to break them into their vertical and horizontal components to do calculations with them Look at the webpage from a climbing website forces forces

90N Force at an angle of 30degrees 90 N

First To find F v To find F H Now try Resolution of forces questions 1-4