# Soil Mechanics Questions and Answers – Stress Distribution – Contact Pressure

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This set of Basic Soil Mechanics Questions and Answers focuses on “Stress Distribution – Contact Pressure”.

1. Contact pressure is between __________
a) base of footing and underlying soil mass
b) wall and column
c) slab and wall
d) wall and beam

Explanation: Contact pressure is defined as the vertical pressure acting at the surface of contact between the base of footing and the underlying soil mass.

2. Contact pressure is the ratio of ___________
a) area to normal load
d) normal load to true contact area

Explanation: Contact pressure is defined as the vertical pressure acting at the surface of contact between the base of footing and the underlying soil mass.
∴ $$Contact \,pressure=\frac{normal \,load}{true \,contact \,area}.$$

3. Contact pressure can be called scratch hardness only in case of __________
a) elastic contact
b) semi-elastic contact
c) plastic contact
d) semi-plastic contact

Explanation: Contact pressure may be also called scratch hardness only in case of plastic contact. Scratch hardness is used to determine the hardness of a material by its scratch resistance.
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4. The following diagram represents the contact pressure of __________

a) real elastic material
b) intermediate soil
c) cohesionless soil
d) gravel

Explanation: In the case of real elastic material, the theoretical intensity of contact pressure at the centre is q/2 and infinite at the outer edges. But at the outer edges, due to local yielding, causes the redistribution of pressure making it finite at the edges.

5. The following diagram represents the contact pressure of __________

a) real elastic material
b) intermediate soil
c) cohesionless soil
d) gravel

Explanation: In the case of intermediate soil, when the footing is neither flexible nor perfectly rigid, the underlying soil posses both cohesion and friction. Therefore, the contact pressure lies in between extreme conditions of uniform and non- uniform distribution for flexible and rigid footing.

6. The following diagram represents the contact pressure of __________

a) real elastic material
b) intermediate soil
c) cohesionless soil
d) gravel

Explanation: In the case of cohesionless soil, no resistance to deformation is offered at the outer edges making it zero at the outer edges. The pressure is parabolic with maximum value at the centre.

7. Find the load at depth 10m for a uniformly loaded circular area of radius 1000m. k=1. The vertical pressure σz is 80 kN/m2.
a) 51kN/m2
b) 54 kN/m2
c) 80 kN/m2
d) 12kN/m2

Explanation: Given,
uniformly loaded circular area of radius a=10m
depth z=1000m
vertical pressure σz = 80 kN/m2
The Boussinesq’s vertical pressure σz under a uniformly loaded circular area is given by,
$$σ_z=q\left[1-[\frac{1}{1+(\frac{a}{z})^2}]^\frac{3}{2}\right]$$
∴ $$80=q\left[1-[\frac{1}{1+(\frac{1000}{10})^2}]^\frac{3}{2}\right]$$
∴ q=80 kN/m2.

8. Find the depth z for a uniformly loaded circular area of 80 kN/m2 load and radius of 50m. k=0.9160.
a) 2m
b) 4m
c) 25m
d) 50m

Explanation: Given,
uniformly loaded circular area of radius a=50m
k=0.9160.
The Boussinesq’s influence factor k under a uniformly loaded circular area is given by,
$$k=\left[1-\left[\frac{1}{1+(\frac{a}{z})^2}\right]^\frac{3}{2}\right]$$
∴ $$0.9160=\left[1-\left[\frac{1}{1+(\frac{50}{z})^2}\right]^\frac{3}{2}\right]$$
∴ z=25m.

9. If the contact pressure is 14 kN/m2, then find the load for 50 m2.
a) 500kN
b) 600kN
c) 700kN
d) 800kN

Explanation: Given,
contact pressure is 14 kN/m2
area =50 m2
$$Contact\, pressure=\frac{normal\, load}{true \,contact\, area}$$
normal load= Contact pressure* true contact area

10. If a UDL of 70 kN/m2 is acting at a rectangular area of 25 m2, then the contact pressure is _______
a) 51kN/m2
b) 54 kN/m2
c) 80 kN/m2
d) 70 kN/m2

Explanation: Given,
UDL of 70 kN/m2
area = 25 m2
$$Contact\, pressure=\frac{normal\, load}{true \,contact\, area}$$
Since for every m2, load of 70 kN acts. Therefore the contact pressure is 70 kN/m2.

11. The contact pressure of a footing was found to be 85 kN/m2 for a load of 212.5 kN. What will be the contact area?
a) 1 m2
b) 2.5 m2
c) 3 m2
d) 3.5 m2

Explanation: Given,
contact pressure=85 kN/m2
load of 212.5 kN
$$Contact\, pressure=\frac{normal\, load}{true \,contact\, area}$$
∴ $$true \, contact \,area=\frac{normal load}{contact pressure}$$
Area=212.5/85=2.5 m2.

12. If a footing has a dimension of 1m*1m and load transfer of 20 kN, then the contact pressure is _______________
a) 20 kN/m2
b) 30 kN/m2
c) 50 kN/m2
d) 70 kN/m2

Explanation: Given,
Dimension=1m*1m
Area =1*1=1 m2
$$Contact\, pressure=\frac{normal\, load}{true \,contact\, area}$$
∴ the contact pressure=20/1=20 kN/m2.

13. For a saturated clay, the theoretical intensity of contact pressure at the centre is________
a) q
b) q/2
c) ¾ q
d) q/3

Explanation: The saturated clay is good example of real elastic material. For a real elastic material, the theoretical intensity of contact pressure at the centre is q/2 and infinite at the outer edges. But at the outer edges, due to local yielding, causes the redistribution of pressure making it finite at the edges.

14. If the footing is flexible, then the distribution pressure is uniform.
a) True
b) False

Explanation: The actual contact pressure distribution depends upon flexural rigidity of footing and the elastic properties of the sub-grade. If the footing is flexible, then the distribution pressure is uniform irrespective of the type of sub-grade or under-soil material.

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