1. WORKSHEET 4 BEAMS

2. Q1 tributary area 600mm 2m tributary area for joist = 2 x 0.6 = 1.2 m2
Given that floor joists are at 600mm centres and span 2.0m
between bearers, what is the tributary area for one joist?
tributary area
600mm 2m
tributary area for joist =
2 x 0.6 =
1.2 m2

3. Q2
Given a floor 18 m x 18 m with columns on a 6m x 6m grid,
what is the tributary area for: 6m
(i) an internal column
6 x 6 =
36 m2 6m
(ii) a column on the edge
6 x 3 =
18 m2 6m
(ii) a corner column
3 x 3 =
9 m2

4. Q3
Given the values in the Building Principles Notes for the
Dead Loads of materials (P17), determine the dead load of the
roof/ceiling construction shown below
6mm corrugated fibre cement sheet kN/m2
13mm plasterboard ceiling kN/m2
100 x 50 hardwood 600mm crs - 11 kN /m3
We are after a 1sq m of roof, but the rafters are at 600mm centres so that 1m width of roof will contain 1.67 rafters (1 / 0.6).
0.6
1.67
1.67 x 0.6 = 1.0
Another way of doing this is to say that 1sqm can be achieved
by an area 0.6 wide x 1.67 long (1 / 0.6).
Weight of rafter 1.67m long = 0.1 x 0.05 x 1.67 x 11
= 0.09 kN
Weight of 1 sq m fibre cement = 1 x 0.11
= 0.11 kN
Weight of 1 sq m plasterboard = 1 x 0.22
= 0.22 kN
Total weight of roof/ceiling per sq m
= 0.42 kN / m2
= 0.42 kPa

5. Q4 The roof above spans between roof trusses which are
at 2.5 m centres and span 10m
2.5m
a) sketch the layout described and
indicate the tributary area for
one truss
2.5m
10.0m
b) what is the total load
on one truss? (neglecting the
self-weight of the truss)
Tributary area = 2.5 x 10
= 25 m2
Total load = 25 x 0.42
= 10.5 kN
c) what is load per metre on one truss?
Note:
We have neglected the
self-weight of the truss
Load per metre = 10.5 / 10
=1.05kN / m

6. Q5 What are the two main types of stress involved in beam action? a)
bending b)
shear

7. Q6 In buildings: a) which of the above two (bending & shear)
is more important?
bending b)
why?
have bigger spans relative to loads.
In the design of machines have short spans
with heavy loads and shear more important.

8. Q7 What does shear force do to: a) timber beams?
can cause horizontal splitting along grain b)
steel beams?
not so critical - make sure don’t exceed
allowable shear stress c)
concrete?
tends to cause diagonal tension cracks
near supports

9. Q8 How is shear resisted in concrete beams:
a) steel reinforcement at 450
b) stirrups

10. + - Q9 What is the sign convention for Bending Moment Diagrams for: a)
sagging?
positive - b)
hogging?
negative

11. Q10 a) What does a Shear Force Diagram tell you?
the values of the shear force along the beam
you can see where the maximum shear force
occurs
b) What does a Bending Moment Diagram tell you?
the values of the bending moment along the beam
you can see where the maximum bending moment
occurs and whether it is positive or negative

12. Q11 For each of the Following Loading Conditions a)
Sketch the deflected shape and note where positive
and negative bending moments are expected to occur b)
Find the reactions c)
Draw the Shear Force Diagrams d)
Find the maximum bending moment(s) and
draw the Bending Moment Diagrams
draw the diagrams approximately to scale (i.e. in proportion) and mark
significant values
make use of symmetry and standard Bending Moment coefficients
where appropriate

13. Q11 A & B A B + Deflected Shape + SFD BMD 16 kN 2m 4m 4m UDL 5kN/m
WL/4 = 16 x 4 / 4 =
BMD
+10 kNm
wL2/8 = 5 x 4 x 4 / 8 =

14. Q11 C & D - - C D Deflected Shape SFD BMD 2m 10 kN UDL 5kN/m 2m
R =10 kN
W = w x L
= 5 x 2 = -
10 kN
SFD
+10 kN
+10 kN
-10 kNm
-wL2/2
= -5 x 2 x 2 / 2 =
BMD
-WL = -20 kNm

15. Q11 E SFD + Deflected Shape BMD 5m 20kN 2m 1m A B C D +16 kN -24 kN
TL =
= 40 kN
For reactions
Moments about A
RR x 5 = 20 x x 4
= 120
RR = 24 kN
RL = 16 kN
Moment at B
= 16 x 2
= 32 kNm
Moment at C
= 24 x 1
= 24 kNm
24 kN
Deflected Shape +
16 kN
32 kNm
24 kNm
BMD

16. Q11 F SFD - BMD Deflected Shape 2m 10kN 1m 5kN A B C +15 kN +5 kN
TL =
= 15 kN
For reactions
Moment at A
= 10 x x 2
= 20 kNm
Moment at A
= - 20 kNm
Moment at B
= - 5 x 1
= - 5 kNm -
Deflected Shape
15 kN
-20 kNm
-5 kNm
BMD

17. Q11 G - SFD + BMD 4m 2m 20kN 5kN A C B +12.5 kN -7.5 kN -5 kN
TL =
= 25 kN
For reactions
Take Moment at C
RL x 4 = 5 x x 2
= 70
RL = 17.5kN
RR = 7.5kN
Moment at A
= -5 x 2
= -10 kNm
Moment at B
= 7.5 x 2
= 15kNm
WL/4 = 20x4/4
= 20kNm
20 kNm
-10 kNm
BMD
+15 kNm
7.5 kN +
17.5 kN -
Deflected Shape

18. Q11 H - SFD + BMD 4m UDL 5kN/m 2m A B C -10 kN +12.5 kN -7.5 kN 30kN
TL = 5 x 6
= 30 kN
For reactions
Take Moment at C
RL x 4 = 30 x 3
= 90
RL = 22.5kN
RR = 7.5kN
Moment at A
= -10 x 1
= -10 kNm
Moment at B
= 7.5 x x 2 x 1 =
= 5 kNm
WL/8 = 20x4/8
= 10kNm
-10 kNm
+5 kNm
+~5.6 kNm
10 kNm
BMD
7.5 kN
10kN
20kN +
22.5 kN -
Deflected Shape

19. Q11 H (cont.) BMD (cantilever) wL2/2 = -10 kNm BMD (Simply Supported)
BMD(Comb)

20. Q11 I - - SFD (Cantilevers) Cantilevers SFD Simply Supported (Simply
UDL 5kN/m 2m
SFD
(Cantilevers)
+10 kN
-10 kN
RL = 10 RR = 10 -
10 kN
10kN
Cantilevers
+10 kN
-10 kN
SFD
(Simply
Supported)
RL = 10 RR = 10 +
10 kN
20kN
Simply Supported
+10 kN
-10 kN
SFD
(Combined)
RL = 20 RR = 20 -
20 kN
20kN
10kN
Combined

21. Q11 I (cont.) BMD (cantilevers) BMD (Simply Supported) BMD(Comb)
-10 kNm
-10 kNm
wL2 / 2 = 5 x 2 x 2 / 2
= 10 kNm
BMD
(Simply
Supported)
+10 kNm
wL2 / 8 = 5 x 4 x 4 / 8
= 10 kNm
BMD(Comb)