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

2. Distributed loads

4. 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

5. 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

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

7. Distributed loads Now take moments as before about R A or R B About A 50 x 5 = R B x 10 250 = R B x 10 R B =25 kN 50kN 10m RBRB RARA

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

9. 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

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

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

12. FVFV FHFH

13. F V =20 F H= 34.64 Now take moments about A to find R B

14. F V =20 F H= 34.64 =25N Finally find the vertical and horizontal components of the reaction R A

15. F V =20 F H= 34.64 =25N Finally find the vertical and horizontal components of the reaction R A

16. F V =20 F H= 34.64 =25N Finally find the vertical and horizontal components of the reaction R A

17. F V =20 F H= 34.64 =25N

18. Beam reaction questions p22