Strength of Materials (Concepts)

Flexibility.

Also called compliance, this is the inverse of stiffness and is typically measured in units of meters per Newton.

Spherical pressure vessel.

Any section that passes through the center of the sphere yields the same result.

Proportional limit.

From the origin O to this point, the stress-strain curve is a straight line.

Modulus of Elasticity (Young's Modulus).

Hooke's law states that the strain in a solid is proportional to the applied stress within the elastic limit of that solid. The constant of proportionality, k, is called? (Refer to the formula in the image shown)

Thermal stress.

If thermal deformation is restricted to occur freely, internal forces will develop that oppose the thermal expansion or contraction. The stresses caused by these internal forces are known as:

Coefficient of thermal expansion.

In the formula for thermal strain shown, what does the symbol, the Greek letter alpha, represent?

Polar moment of inertia.

It defines the resistance of a cross-section to torsional deformation, due to the shape of the cross section.

Punching shear stress.

It is a failure mechanism in structural members like slabs and foundation by shear under the action of concentrated loads.

Torque.

It is a moment which tends to cause twisting.

Spherical pressure vessel.

It is a special case of a cylindrical vessel.

Stress.

It is defined as the unit strength of a material per unit area or simply, unit strength.

Shear strain.

It is the change in angle at the corner of an original rectangular element.

Working stress.

It is the maximum safe axial stress used in design. Also called the allowable stress.

Yield point.

It is the point at which the material will have an appreciable elongation or yielding without any increase in load.

Strain.

It is the ratio of the change in length caused by the applied force to the original length. Also known as unit deformation.

Modulus of Elasticity (G).

It is the ratio of the shear stress and the shear strain and is denoted as G.

Stiffness.

It is the ratio of the steady force acting on an elastic body to the resulting displacement.

Normal strain.

It is the strain elongation or contraction per unit length (tensile or compressive).

Rupture strength.

It is the strength of the material at rupture. This is also known as the breaking strength.

Rupture strength.

It is the stress at which failure occurs.

Torsion.

It is twisting of an object caused by a moment acting about the object's longitudinal axis.

There is no deformation in the lateral directions when a longitudinal tensile force is applied.

Most materials have a Poisson's ratio ranging from 0 to 0.5. What does it mean if the ratio is 0 such as a bottle cork?

A rod of unit mass suspended vertically from one end with an elongation due to self weight.

On what conditions may this formula for axial (normal) strain be used?

The loads must be axial, the bar doesn't have a uniform cross-sectional area, and the stress must not exceed the proportional limit.

On what conditions may this formula for axial (normal) strain be used?

The loads must be axial, the bar must have a uniform cross-sectional area, and the stress must not exceed the proportional limit.

On what conditions may this formula for axial (normal) strain be used?

Spherical pressure vessel.

Preferred for storage of high pressure fluids.

Simple stress.

Quantity that describes the distribution of internal forces within a body.

It is equal to the slope of the stress-strain diagram from point O to P.

Referring to the stress-strain diagram, which of the following statements is true regarding the Modulus of Elasticity?

Stress-strain diagram.

The graph of such quantities with the stress along the y-axis and the strain along the x-axis is called the:

Elastic limit.

The limit beyond which the material will no longer go back to its original shape when the load is removed.

Spherical pressure vessel.

The spherical geometry is twice as efficient in terms of wall stress.

Ultimate strength.

This is the maximum ordinate in the stress-strain diagram. Also known as tensile strength.

Poisson's ratio (v).

This is the parameter that defines how much the material will deform in the lateral directions.

Shear stress.

This stress, also called tangential stress, is commonly found in bolts, pins, and rivets used to connect various structural members.

The ratio of radius (r) to the wall thickness (t) is greater than or equal to 10.

What is considered as a general rule to classify pressure vessels as thin walled?

Change in length due to temperature change.

What is the formula shown?

Circumferential/tangential stress.

What is the formula shown?

Double shear stress.

What is the formula shown?

Generalized Hooke's Law for Multi-axial Loading.

What is the formula shown?

Generalized Hooke's Law for Uni-axial Loading.

What is the formula shown?

Longitudinal/axial stress.

What is the formula shown?

Modulus of Elasticity (G).

What is the formula shown?

Poisson's ratio (v).

What is the formula shown?

Polar moment of inertia for hollow cylindrical shaft.

What is the formula shown?

Polar moment of inertia for solid cylindrical shaft.

What is the formula shown?

Punching shear stress.

What is the formula shown?

Shear strain.

What is the formula shown?

Shear stress.

What is the formula shown?

Simple/normal stress.

What is the formula shown?

Single shear stress.

What is the formula shown?

Spherical pressure vessel stress.

What is the formula shown?

Stiffness.

What is the formula shown?

Strain.

What is the formula shown?

The relationship between the Shear Modulus and Modulus of Elasticity and Poisson's Ratio.

What is the formula shown?

The relationship between the shearing deformation and the applied shearing force.

What is the formula shown?

Thermal strain.

What is the formula shown?

Thermal stress if the wall where the rod is attached yields a distance x.

What is the formula shown?

Thermal stress.

What is the formula shown?

Torsion angle (Angle of twist).

What is the formula shown?

Torsional shearing strain.

What is the formula shown?

Working stress.

What is the formula shown?

Spheres are much more costly to manufacture than cylindrical vessels.

What is the major drawback of spherical pressure vessels in terms of construction?

Circumferential/tangential stress.

What stress is described in the image shown?

Longitudinal/axial stress.

What stress is described in the image shown?

Spherical pressure vessel stress.

What stress is described in the image shown?

Statically determinate structure.

What type of structure is classified as in the image shown?

Statically indeterminate structure.

What type of structure is classified as in the image shown?

No internal forces will be induced in the body. There will be strain, but no stress.

What would result if thermal deformation is permitted to occur freely?

Internal forces will develop that oppose the thermal expansion or contraction.

What would result if thermal deformation is restricted to occur freely?

An element subject to shear does not change in length but undergoes a change in shape.

Which of the following is true about shearing deformation?

It is common practice to consider a material as acceptable for use if the stress of the material does not exceed beyond the yield strength.

Which of the following statement best describes the image shown?

The rivet is said to be in double shear.

Which of the following statement describes the condition of the rivet shown in the picture?

The rivet is said to be in single shear.

Which of the following statement describes the condition of the rivet shown in the picture?

The normal stress in the walls of the container is proportional to the pressure and radius of the vessel and inversely proportional to the thickness of the walls.

Which of the following statement describes the formula generally used for thin walled pressure vessels?

Force is applied perpendicular to the cross-sectional area of the material.

Which of the following statements best describes normal stress?

Compressed gas storage tanks designed to hold gases or liquids at a pressure substantially different from the ambient pressure.

Which of the following statements best describes pressure vessels such as aircraft fuselages, soda cans, etc.?

The internal forces that develop within are oriented parallel to the bar's cross section.

Which of the following statements best describes shear stress?

Pressure vessels are subjected to tensile forces within the walls of the container.

Which of the following statements best describes the forces acting on thin walled pressure vessels?

A spherical pressure vessel has approximately twice the strength of a cylindrical pressure vessel with the same wall thickness.

Which of the following statements best describes the strength of spherical pressure vessels?

The distribution of stresses on the sphere's surfaces, both internally and externally are equal.

Which of the following statements best describes the stress distribution of spherical pressure vessels?

It is the maximum stress that may be developed such that there is no permanent or residual deformation when the load is entirely removed.

Which of the following statements best describes the stress of the elastic limit of a material?

The effect of internal forces is equal to the effect of the external forces.

Which of the following statements best describes uniaxial loading?

Within the proportional limit of the stress-strain diagram, the stress is directly proportional to strain.

Which of the following statements defines the Hooke's Law?

The forces acting are the total pressures caused by the internal pressure (p) and the total tensions in the walls (T).

Which of the following statements describes the forces acting on a pressure vessel that undergoes a circumferential or tangential stress?

The total force acting at the rear of the tank (F) must be equal to the total longitudinal stress on the wall.

Which of the following statements describes the forces acting on a pressure vessel that undergoes a longitudinal or axial stress?

Cracked or damaged vessels can result in leakage or rupture failures.

Which of the following statements emphasizes the importance of the study of strength of materials on thin walled pressure vessels?

It is the initial area of the material. It is assumed to have a constant value throughout the tensile test.

Which of the following statements explains the area of the formula for calculating rupture stress as shown in the image?

The area of the material is instantaneous. It changes throughout the tensile test.

Which of the following statements explains the area of the formula for calculating rupture stress as shown in the image?

Rupture strength is less than the ultimate strength.

Which of the following statements is true regarding the strength of structural steel?

This deformation is isotropic (the same in every direction) and proportional to the temperature change.

Which one of the following statements best describes thermal strain?

Reactions and internal forces can be determined solely from free-body diagrams and equations of equilibrium without knowing the properties of the materials.

Which one of the following statements defines statically determinate structures?

In addition to the equilibrium consideration, equations pertaining to the displacement of the structure, called equations of compatibility, and the relations between forces and displacements are usually needed.

Which one of the following statements defines statically indeterminate structures?

When you apply a load to a material in one direction, the material will also deform in the lateral directions.

Which one of the following statements describes the Poisson's ratio of a material?

An increase in temperature results in expansion, whereas a temperature decrease produces contraction.

Which one of the following statements describes the relationship between temperature and material deformation?

Shear stresses increase linearly with the distance from the center of the cross section, with the maximum shear stress occurring on the outer surface.

Which one of the following statements is true regarding torsional shearing stress?

The lateral strain is uniform throughout the cross section and is the same in any direction in the plane of the cross section.

Which one of the statements best describes the Poisson's ratio of isotropic materials?

They are materials with negative Poisson's ratio and the soles of the shoes are the best example.

Which one of the statements is true about Auxetic Materials?

The higher the stiffness, the higher the force required to cause a displacement in the structure.

Which one of the statements is true regarding the stiffness of a material?

It is the stress at which permanent set (permanent deformation) may occur.

Why is it that the stress at the yield point is selected as the basis for determining working stress in structural steel?

The tangential stress is twice larger than the longitudinal stress.

Why is it very common for cylindrical pipes / pressure vessels to rupture first in the axial or longitudinal direction?