1. MASS DENSITY AND VOLUME

2. AREAS OF SHAPES RECTANGLE = L * B CIRCLE = ((π* D2)/4)
TRIANGE =(0.5 B* H) B D H B

3. 2) CIRCULAR ((π* D2)/4) * H)
VOLUMES OF SHAPES
1) RECTANGULAR L*B*H
2) CIRCULAR ((π* D2)/4) * H)
3 TRIANGULAR (0.5 B* H * L)

4. THE CONCEPT OF MASS , DENSITY AND LOADING
DENSITY IS THE MASS OF AN OBJECT / m3
MASS =VOLUME * DENSITY =Kg
LOAD= KG * = NEWTONS
LOAD IN KN = NEWTONS /1000 =KN

5. DENSITY
DIFFERENT MATERIALS HAVE DIFFERENT DENSITIES AND DIFFERENT MASSES / VOLUME
WATER =1000 Kg / m3
CONCRETE =2400Kg / m3
STEEL =6800Kg / m3
WOOD =1650 Kg / m3

6. Rectangular shapes

7. SECTIONAL VIEWS OF A BLOCK

8. A SIMPLE EXAMPLE VOLUME =L*B*H 1*1*2.5 = 2.5m3 MASS = V* DENSITY
WORK OUT THE FORCE THAT THE BLOCK SHOWN BELOW EXERTS DUE TO ITS MASS AND THE GRAVITATIONAL PULLOF THE EARTH IF IT HAS THE SAME DENSITY AS WATER
VOLUME =L*B*H
1*1*2.5 = 2.5m3
MASS = V* DENSITY
2.5m3 *1000kgs =2500kgs
LOAD = MASS*9.81
(2500* 9.81)/1000 =24.53KN

9. WORK OUT THE PRESSURE EXERTED ON THE GROUND BY THE SOLID CONCRETE BLOCK

10. rectangular Area = L*B 10*5 = 50m2 Volume L*B*H 10*5 *2 =100m3
Mass = Volume * Density
100*2400 = kgs
Load = (Mass *9.81 )/1000=Kn
(240000*9.81)/1000= Kn
Pressure = F/A
2354.4/ 50= Kp

11. WORK OUT THE PRESSURE EXERTED ON THE GROUND BY THE CONCRETE TANK

12. Tank Volume L*B*H concrete (10*5 *2)- ( 9*4*1.5)=46m3 Mass concrete
46 *2400 = kgs
Load
(110400*9.81)/1000= kn
Pressure
/ 50 =21.66 kpa

13. WORK OUT THE PRESSURE EXERTED ON THE GROUND BY THE CONCRETE TANK FILLED WITH WATER

14. Tank filled with water Volume L*B*H concrete
Mass concrete
46 *2400 = kgs
Volume water
( 9*4*1.5)=54 m3
Mass of water
54*1000=54000 kgs
Load
(( )*9.81)/1000=
Pressure = / 50 = 32.26

15. FORCES THAT STRUCTURES EXERT ON THE GROUND
FROM THE DRAWING
OF A CONCRETE
FOUNDATION WORK
OUT THE FOLLOWING
(DENSITY = 2400Kg/m3)
ITS VOLUME
ITS MASS
ITS LOAD

16. MODEL ANSWER
Vol = (1.5* 0.4*0.6) – (1 *0.6 *0.2)+ ( 0.4*0.6*0.25)= 0.3m3
Mass = 0.3 *2400= 720 kgs
Load = ( 720*9.81)/ 1000 = 7.06 kn

17. Cylinders

18. SECTIONAL VIEWS OF A CYCLINDER
THREE DIMENSIONAL
SECTIONAL
PLAN

19. Work out the load Of the structure due To gravity ( P 2300)
0.5m
hole
((π* 6.22)/4)- ((π* 52)/4) *0.5
Volume =5.3m3
Mass = 5.3*2300=12190 kg
Load = (12190*9.81)/1000
= 120 Kn

20. Diameter 3.5m

21. Total vol concrete = 84.9- 65.34 = 19.56m3
A circular tank is to be filled with sand density 1234 find the pressure the tank exerts on the ground
A) when empty
B) when fill of sand
xsa cylinder = 28.3m2 vol = 28.3*3=84.9
xsa hole = 23.76m2 vol = 23.76*2.75=65.34
Total vol concrete = = 19.56m3
Mass = * 2400 = kgs
Load =( 46944*9.81)/ 1000= kn
Pressure = / 28.3 = kpa
Mass sand = *1234 =
Load = ( *9.81)/1000= kn
Pressure = ( )/ 28.3=44.22kpa

22. What is the mass of
The structure
What is the pressure
On the ground.
Density of concrete
= 2400kg/m3
Empty
When cylinders half
filled with sand
P = 1340 kg/m3

23. Rec V= 15 *8 *1 = 120 m 3
CIR V= (((π * 3 2 /4 )-(π * /)4 ))*2 ) * 2) = m 3
MASS CON = * 2400 = kgs
LOAD = ( *9.81)/1000= kn
PRESSURE = /(8*15 ) = 27.71
SAND V = (π * /)4 )*2 = 3.53m 3
LOAD = (3.53 *1340 * 9.81 )/1000= 46.4 KN
TOTAL PRESSURE = ( ) /(8*15 )= 28.1

24. Plan What upward load can the anchor Resist
What pressure does the structure
Exert on the ground

25. Sectional view Density soil =1859 kg / m3 Density con =2358 kg / m3
Natural ground

26. Volume of base = (π* 182)/4)*2)-(π* 142)/4)*1.5)= 278.03
Model answer
Volume of base = (π* 182)/4)*2)-(π* 142)/4)*1.5)=
Volume of column = (6*6*2 ) – (4*3*2) = 48
Volume of sand = (4*3*2) =24
Total volume = =
Mass empty = *2358 =
Mass sand = 24 * 1859 = 44616
Total mass = kgs
Load = ( *9.81) /1000 = kn
Pressure = )/(π* 142)/4)=51.83

27. Examples
A concrete footing consists of a circular base and a hollow square column. The base has a diameter of 3,0 m and is 500 mm thick. The external dimensions of the 1,5 m high column are mm x 500 mm with a wall thickness of 100 mm. Concrete has a density of kg/m3 and the footing is loaded as shown.
Calculate the pressure exerted by the concrete footing on the ground below.

29. 3d view

30. QUESTION ONE (12 marks)
Vbase = x 32 x 0,5 = 3,534 m3 (1 mark)
Vcol = [(0,5 x 0,5) – (0,3 x 0,3)] x 1,5 = 0,24 m3 (1 mark)
Vtot = 3,774 m3
Wconc = 2400 x 3,774 x 9,81 / 1000 = 88,856 kN (2 marks)
Total downward load = 88, sin = 103,676 kN (2 marks)
Area = x 32 = 7,069 m2 (2 marks)
Pressure = Force / Area = 103,676 / 7,069 = 14,666 kPa (2 marks)

31. Example 2
The drawing BELOW shows the plan view and sectional view of a circular concrete tank if the density of concrete and water is 2345 kg/ m3 and 1000kg/ m3 respectively calculate the following.
The resultant load of the structure
the pressure exerted by the tank on the ground when it is filled with water

32. 4.2m
4.2m

33. Vol cylinder = (( π* 4.62)/4 )*2.6)) = 43.21
Vol hole = (( π* 4.22)/4 )*2.5)) = 34.61
Vol concrete = – =
Load =( 8.57 * 2345 * 9.81 )/1000 = kn
Vol w = 34.64
Load = *9.81 =
Tot load = =
Pressure /(( π* 4.62)/4 )= kpa