Distributed loads Loads are not always point loads Sometimes there are uniformly distributed loads on structures

Distributed loads

Loads are not always point loads Sometimes there are uniformly distributed loads (UDLs) on structures What are the reactions at the supports A and B 5kNm -1 10m RBRB RARA

Distributed loads First work out the total load 5kNm -1 x 10m = 50kN This can be considered as acting at the midpoint of the UDL 50kN 10m RBRB RARA

Distributed loads Now take moments as before about R A or R B 50kN 10m RBRB RARA

Distributed loads Now take moments as before about R A or R B About A 50 x 5 = R B x = R B x 10 R B =25 kN 50kN 10m RBRB RARA

Distributed loads 50kN 10m R B =25 kN RARA ∑ F v = 0 R A + R B = 50 R A + 25 = 50 R A =25

10m 10kNm -1 2m 50kN 1. 5m 20kNm -1 2kN 3. 5m 0.5m 6m 50kN m -1 2m 10kN 2. 2m 6m 50kNm -1 2m 4. 2m 50kN 3m UDL Questions- Find the reactions of the simply supported beams

The roller can only have a vertical reaction R b The hinge can supply a reaction force R A at any angle

Start by finding the vertical and horizontal components of the 40N force Then take moments about A to find R B FVFV FHFH

FVFV FHFH

F V =20 F H= Now take moments about A to find R B

F V =20 F H= =25N Finally find the vertical and horizontal components of the reaction R A

F V =20 F H= =25N Finally find the vertical and horizontal components of the reaction R A

F V =20 F H= =25N Finally find the vertical and horizontal components of the reaction R A

F V =20 F H= =25N

Beam reaction questions p22