# Material Deformation and Equilibrium Quiz

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## 75 Questions

Volume strain

Shearing strain

Shearing stress

### What is the angular displacement of the cylinder from the vertical called?

Tangential displacement

Shearing strain

Hydraulic stress

Volume strain

Volume strain

Shearing strain

### What is the strain produced by a longitudinal force called?

Longitudinal strain

Tensile stress

### What is the SI unit of stress?

N m$^{-2}$ or pascal (Pa)

### What is the dimensional formula of stress?

[ ML$^{-1}$T$^{-2}$ ]

### What is the change in the length of a body to the original length when it is subjected to tensile or compressive stress?

Longitudinal strain

### What is the term for the restoring force per unit area when a cylinder is compressed under the action of applied forces?

Compressive stress

Stretched

### What is the restoring force per unit area known as when a body is subjected to tensile or compressive stress?

Longitudinal stress

Shear stress

Strain

### What is the restoring force per unit area known as when a body is subjected to forces causing change in volume?

Volumetric stress

True

True

False

True

True

True

False

False

False

False

False

False

True

True

False

True

True

True

True

True

### Define stress and give its SI unit and dimensional formula.

Stress is the restoring force per unit area developed in a body when subjected to deforming forces. Its SI unit is N m$^{-2}$ or pascal (Pa) and its dimensional formula is [ML$^{-1}$T$^{-2}$].

### What are the three ways in which a solid may change its dimensions when an external force acts on it?

A solid may change its dimensions by stretching (tensile stress), compressing (compressive stress), or undergoing shearing (shearing stress) when an external force acts on it.

### Explain the concept of longitudinal strain.

Longitudinal strain is the change in the length $\Delta L$ to the original length $L$ of the body when it is subjected to tensile or compressive stress.

### What is the restoring force per unit area known as when a body is subjected to tensile or compressive stress?

The restoring force per unit area is known as longitudinal stress when a body is subjected to tensile or compressive stress.

### Define the strain produced by a shearing force and give its name.

The strain produced by a shearing force is called shearing strain, and it is the ratio of the relative displacement of the faces to the length of the body.

### Define shearing strain and provide its mathematical representation.

Shearing strain is the strain produced by a shearing force and is defined as the ratio of the relative displacement of the faces $\Delta x$ to the length of the cylinder $L$. Mathematically, shearing strain is represented as $\Delta = \frac{\Delta x}{L}$.

### What is volume strain and how is it mathematically expressed?

Volume strain is the strain produced by a hydraulic pressure and is defined as the ratio of the change in volume $\Delta V$ to the original volume $V$. Mathematically, volume strain is represented as $\Delta = \frac{\Delta V}{V}$.

### Explain the relationship between angle $\theta$ and the tangent of $\theta$ in the context of shearing strain.

In the context of shearing strain, when the angle $\theta$ is very small, the relationship between $\theta$ and the tangent of $\theta$ can be approximated as $\tan \theta \approx \theta$. This means that if $\theta = 10^\circ$, for example, there is only a 1% difference between $\theta$ and $\tan \theta$.

### What is hydraulic stress and how is it related to the applied hydraulic pressure?

Hydraulic stress is the internal restoring force per unit area developed in a body when subjected to a hydraulic pressure. Its magnitude is equal to the applied hydraulic pressure (applied force per unit area).

### Explain the concept of longitudinal strain and provide its mathematical expression.

Longitudinal strain is the strain produced by a longitudinal force and is defined as the ratio of the change in length $\Delta L$ to the original length $L$. Mathematically, longitudinal strain is represented as $\Delta = \frac{\Delta L}{L}$.

restoring force

### The SI unit of stress is N m$^{-2}$ or pascal (Pa) and its dimensional formula is

[ ML$^{-1}$T$^{-2}$ ]

tensile

longitudinal

hydraulic

tensile

compressive

tangential

tensile

hydraulic

### Longitudinal strain is defined as the ratio of change in length to the original length of the cylinder.

longitudinal strain $\Delta = \frac{\Delta L}{L}$

### Shearing strain is defined as the ratio of relative displacement of the faces to the length of the cylinder.

shearing strain $\Delta = \frac{\Delta x}{L} = \tan \theta$

volume

### The restoring force per unit area developed due to the applied tangential force is known as _____ stress.

tangential or shearing

true

true

volume

tensile

compressive

longitudinal

### Match the following terms with their definitions:

Shearing strain = Ratio of relative displacement of the faces to the length of the cylinder Hydraulic stress = Restoring force per unit area developed due to the applied hydraulic pressure Volume strain = Ratio of change in volume to the original volume Longitudinal strain = Ratio of change in length to the original length of the cylinder

### Match the following stress types with their descriptions:

Tangential stress = Restoring force per unit area developed due to the applied tangential force Compressive stress = Restoring force per unit area developed when a body is compressed under the action of applied forces Lateral stress = Restoring force per unit area developed when a body is stretched by two equal forces applied normal to its cross-sectional area Hydraulic stress = Restoring force per unit area developed due to the applied hydraulic pressure

### Match the following concepts with their mathematical representations:

Shearing strain = $\Delta = \frac{\Delta x}{L}$ Volume strain = $\Delta = \frac{\Delta V}{V}$ Longitudinal strain = $\Delta = \frac{\Delta L}{L}$ Tangential stress = Restoring force per unit area developed due to the applied tangential force

### Match the following stress types with their applications:

Tangential stress = Applied tangential force Compressive stress = Forces causing change in volume Lateral stress = Two equal forces applied normal to the cross-sectional area Hydraulic stress = Fluid under high pressure

### Match the following terms with their examples:

Shearing strain = Book pressed with the hand and pushed horizontally Hydraulic stress = Solid sphere placed in fluid under high pressure Volume strain = Solid sphere compressed uniformly on all sides Longitudinal strain = Cylinder stretched by two equal forces applied normal to its cross-sectional area

## Study Notes

### Deformation and Stress

• When a body is subjected to a deforming force, it is deformed to a small or large extent depending on the material and magnitude of the force.
• The deformation may not be visually noticeable, but it is present.
• A restoring force is developed in the body, equal in magnitude but opposite in direction to the applied force.

### Stress

• Stress is the restoring force per unit area.
• The formula for stress is: Stress = F/A, where F is the force applied normal to the cross-section and A is the area of the cross-section.
• The SI unit of stress is N m⁻² or Pascal (Pa).
• The dimensional formula of stress is [ML⁻¹T⁻²].

### Types of Stress

• There are three ways a solid may change its dimensions when an external force acts on it.
• Tensile stress occurs when a body is stretched by forces applied normal to its cross-sectional area.
• Compressive stress occurs when a body is compressed under the action of applied forces.
• Both tensile and compressive stress can be termed as longitudinal stress.

### Strain

• Longitudinal strain is the change in length (∆L) to the original length (L) of the body.
• Longitudinal strain occurs when there is a change in the length of the body due to tensile or compressive stress.

Test your knowledge of material deformation and equilibrium with this quiz. Explore the concepts of deforming forces, restoring forces, and material behavior under external forces.

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