Distributed loads

Loads are not always point loadsSometimes there are uniformly distributed loads on structures

Distributed loads

Distributed loads

Distributed loads

Loads are not always point loadsSometimes there are uniformly distributed loads (UDLs) on structures

What are the reactions at the supports A and B

5kNm-1

10m RBRA

Distributed loads

First work out the total load5kNm-1 x 10m = 50kNThis can be considered as acting at the midpoint of the UDL

50kN

10m RBRA

Distributed loads

Now take moments as before about RA or RB

50kN

10m RBRA

Distributed loadsNow take moments as before about RA or RB

About A

50 x 5 = RB x 10

250 = RB x 10 RB =25 kN

50kN

10m RBRA

Distributed loads

50kN

10m RB =25 kNRA

∑ Fv = 0

RA + RB = 50

RA + 25 = 50RA =25

10m

10kNm-1

2m

50kN1.

5m

20kNm-12kN3.

5m0.5m

6m

50kNm-1

2m

10kN2.

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 Rb

The hinge can supply a reaction force RAat any angle

Start by finding the vertical and horizontal components of the 40N force

Then take moments about A to find RB

FV

FH

FV

FH

FV=20

FH=34.64

Now take moments about A to find RB

FV=20

FH=34.64

=25NFinally find the vertical and horizontal components of the reaction RA

FV=20

FH=34.64

=25N

Finally find the vertical and horizontal components of the reaction RA

FV=20

FH=34.64

=25N

Finally find the vertical and horizontal components of the reaction RA

FV=20

FH=34.64

=25N

Beam reaction questions p22