75 Questions
What is the strain produced by a hydraulic pressure called?
Volume strain
What is the strain defined as the ratio of relative displacement of the faces to the length of the cylinder?
Shearing strain
What is the restoring force per unit area developed due to the applied tangential force known as?
Shearing stress
What is the angular displacement of the cylinder from the vertical called?
Tangential displacement
What is the strain produced by a shearing force called?
Shearing strain
What is the restoring force per unit area developed due to the applied hydraulic pressure known as?
Hydraulic stress
What is the ratio of change in volume to the original volume called?
Volume strain
What is the strain defined as the ratio of change in dimension to the original dimension?
Volume strain
What is the strain produced by the applied tangential force called?
Shearing strain
What is the strain produced by a longitudinal force called?
Longitudinal strain
What is the restoring force per unit area when a body is stretched by two equal forces applied normal to its cross-sectional area?
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
In which way does a solid change its dimensions when an external force acts on it in Fig. 8.1(a)?
Stretched
What is the restoring force per unit area known as when a body is subjected to tensile or compressive stress?
Longitudinal stress
What is the restoring force per unit area when a body is subjected to shearing forces?
Shear stress
What is the term for the change in the dimensions of a solid when an external force acts on it?
Strain
What is the restoring force per unit area known as when a body is subjected to forces causing change in volume?
Volumetric stress
Stress is defined as the restoring force per unit area developed in a body when subjected to deforming forces.
True
The SI unit of stress is N m$^{-2}$ or pascal (Pa).
True
Longitudinal stress can also be referred to as compressive stress.
False
The change in the length of a body to the original length when it is subjected to tensile or compressive stress is known as longitudinal strain.
True
The restoring force per unit area developed due to the applied tangential force is known as shear stress.
True
The restoring force per unit area developed when a body is stretched by two equal forces applied normal to its cross-sectional area is known as tensile stress.
True
The restoring force per unit area when a body is subjected to shearing forces is known as compressive stress.
False
The strain produced by the applied tangential force is called lateral strain.
False
The change in the length of a cylinder when it is stretched by two equal forces applied normal to its cross-sectional area is known as lateral strain.
False
The ratio of change in volume to the original volume is called longitudinal strain.
False
Longitudinal strain is defined as the ratio of change in length to the original length of the cylinder.
False
When a solid sphere is placed in a fluid under high pressure, it undergoes shearing strain.
False
The strain produced by a hydraulic pressure is called volume strain.
True
The angular displacement of the cylinder from the vertical is nearly equal to its tangent when the angle is very small.
True
The restoring force per unit area developed due to the applied tangential force is known as hydraulic stress.
False
The restoring force per unit area developed due to the applied tangential force is known as tangential stress.
True
The volume strain has no units or dimensional formula.
True
The strain produced by a shearing force is called shearing strain.
True
The restoring force per unit area developed due to the applied tangential force is known as tangential stress.
True
The restoring force per unit area in the case of hydraulic compression is equal in magnitude to the hydraulic pressure.
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 $\Delta = \frac{\Delta L}{L}$.
______ is equal in magnitude but opposite in direction to the applied force
restoring force
The SI unit of stress is N m$^{-2}$ or pascal (Pa) and its dimensional formula is
[ ML$^{-1}$T$^{-2}$ ]
The restoring force per unit area in this case is called ______ stress
tensile
The change in the length ∆L to the original length L of the body is known as ______ strain
longitudinal
The restoring force per unit area when a body is subjected to forces causing change in volume is known as ______ stress
hydraulic
There are three ways in which a solid may change its dimensions when an external force acts on it. These are shown in Fig. 8.1. In Fig.8.1(a), a cylinder is stretched by two equal forces applied normal to its cross-sectional area. The restoring force per unit area in this case is called ______ stress
tensile
The restoring force per unit area when a body is subjected to shearing forces is known as ______ stress
compressive
The restoring force per unit area developed due to the applied tangential force is known as ______ stress
tangential
The restoring force per unit area developed when a body is stretched by two equal forces applied normal to its cross-sectional area is known as ______ stress
tensile
The restoring force per unit area developed due to the applied hydraulic pressure is known as ______ stress
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 $\Delta = \frac{\Delta x}{L} = \tan \theta$
The strain produced by a hydraulic pressure is called _____ strain.
volume
The restoring force per unit area developed due to the applied tangential force is known as _____ stress.
tangential or shearing
The restoring force per unit area in the case of hydraulic compression is equal in magnitude to the hydraulic pressure.
true
The angular displacement of the cylinder from the vertical is nearly equal to its tangent when the angle is very small.
true
_____ strain has no units or dimensional formula.
volume
The restoring force per unit area when a body is stretched by two equal forces applied normal to its cross-sectional area is known as _____ stress.
tensile
The restoring force per unit area when a body is subjected to shearing forces is known as _____ stress.
compressive
The change in the length of a body to the original length when it is subjected to tensile or compressive stress is known as _____ strain.
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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