Practice Questions

When the temperature of a cantilever beam is increased, no thermal stresses will be developed because there is no restriction to expansion at one end. Thermal stress only occurs when there is external force preventing free expansion or contraction. An increase in temperature produces positive thermal strain and an increase in length, but without restriction, there will be no thermal stresses.

Hooke's law up to the proportional limit, not the elastic limit. Yield stress is the stress at which a material elongates without an increase in load. Toughness is represented by the area under the curve.

Hooke's law is followed up to the elastic limit.

The stress at which a material elongates without an increase in load is called as yield stress.

Toughness is usually represented by the area under a stress

Elasticity is the property of a material to regain its original shape after deformation when external forces are removed. Plasticity is the ability of a material to undergo some degree of permanent deformation without rupture. Durability is the ability of a product to perform its required function over a lengthy period under normal conditions.

The correct answer is strain, which is a initial dimensionless quantity and is expressed as the change in dimension divided by the initial dimension.

Tensile stress: When axial stress produces tension in the body it is known as tensile stress.
Compressive stress: When axial stress produces compression in the body it is known as compressive stress.

The tensile strength of a material is obtained by dividing the maximum load during the test by the original cross- sectional area. $Tensile Strength = \frac {P_{maximum}}{A_{origlnal}}$

The time of fracture and original cross-sectional area

The stress that causes unit strain is known as Modulus of Elasticity (E), which is the ratio of tensile or compressive stress to the corresponding strain. It is also called Young's Modulus and denoted by E = σ /e where σ is tensile or compressive stress and e is strain.

Stress is force per unit area, strain is the measure of deformation experienced by a body. Hooke's law states that stress is directly proportional to strain within the proportionality limit. Young's modulus of elasticity is the constant of proportionality. The stress-strain curve gives the relationship between stress and strain. The limit of proportionality is the stress at which the curve ceases to be a straight line. The elastic limit is that point up to which the material remains elastic.

Within elastic limit, the ratio of stress to strain is called Young's modulus.

Creep is the slow deformation of a material at constant stress and elevated temperature. It occurs in three steps - primary, secondary, and tertiary. Factors affecting creep include material properties, exposure time, exposure temperature, and structural load. Creep resistance can be increased by using high strength and high Young's modulus materials, fine-grain materials for low temperature creep resistance, coarse-grain materials for high temperature creep resistance, and adding refractory metals to alloys for high- temperature creep resistance.

The formula that correctly depicts elongation in a tapered rod is,$ \delta =\frac {4PL}{\pi d_{1} d_{2} E}$

$ \delta =\frac {4PL}{\pi d_{1} d_{2} E}$

Lateral strain is the strain in a direction perpendicular to the applied force

Toughness is the property of a material to absorb energy per unit volume before failure, while withstanding both plastic and elastic deformations. The work done by the external load is absorbed by the material in the form of strain energy. The capacity of a material to absorb this energy per unit volume, before failure, is called toughness. This property is useful for machine components subjected to shock and impact loads.

Young's modulus is the ratio of stress (σ) to strain (ε), and it determines how much a material will deform under a given load. Steel is the most elastic material among the given options, as its Young's modulus (E) is greater than that of rubber, plastic, and brass. Steel has a smaller strain for a given stress compared to rubber, making it more elastic.

A composite bar is made of different materials and both bars strain together under external load. The strain in both bars will be the same when both bars contract equally. The total external load on the bar is equal to the sum of the loads carried by different materials. Strain will be independent of surface area and both materials used in the composite will have different coefficients of thermal expansion

When both bars are subjected to same temperature change

When both bars are subjected to same load

When both bars have the same surface area

Materials that exhibit different elastic properties in different directions are called anisotropic. Orthotropic materials have different elastic properties in perpendicular directions. Isotropic materials exhibit the same elastic properties in all directions at a point. Homogeneous materials have the same elastic properties at all points.

Roller support has a single reaction component, while hinge and fixed supports have multiple reactions.

True stress and engineering stress are two different ways of measuring the stress in a material. True stress is defined as the force per unit area of the material at the instant of deformation, while engineering stress is defined as the force per unit area of the material in its original state.True stress is always greater than the engineering stress in the plastic region

True stress is always less than the engineering stress in the

True stress is always greater than the engineering stress in the plastic region

True stress is equal to the engineering stress in the plastic

True stress is always less than the engineering stress in the elastic region

Malleability is a material's ability to be hammered or rolled into thin sheets without rupture, increasing with temperature. It's the ability to exhibit large deformation or plastic response
when subjected to compressive force. Lead, soft steel, wrought iron, copper, and aluminum are some materials in order of diminishing malleability. Ductility is the ability to be drawn out or elongated before rupture, with percentage elongation or reduction in area before rupture measuring ductility. Brittleness is opposite to ductility, showing little deformation before fracture and failure occurs suddenly.

Can be rolled or hammered into thin sheets

Regains its shape and size after the removal of external forces

Retains the deformation produced under load permanently

Can be drawn into wires with the application of a tensile force

Stress is the internal resistive force to deformation per unit area in solids, while pressure is the amount of force applied per unit area in fluids. Stress can be tensile, compressive, or shear, and can act parallel or perpendicular to the object. The unit of stress is N/m². Pressure is always compressive and acts only perpendicular to the object. Shear stress is used in the viscous flow of fluids.

Young's modulus of elasticity per unit strain

The property of a material by virtue of which, it can be drawn into the wire with the application tensile force is known as ductility.lt is measured as the ratio of elongation of the material at the fracture during the tensile test to the original length, expressed as a percentage.It may also be expressed as the ratio of reduction in the cross-sectional area in the fractured specimen to the original cross-section area.Example, Aluminium, Copper, mild Steel, etc

Fatigue is the failure of a material due to cyclic loads. It involves cracking of materials and structural components due to cyclic stress. Fatigue cracks can be initiated and propagated at stresses below the yield strength of the material. Embrittlement, impact failure, and creep are not related to cyclic loads. Creep is a time-dependent deformation under a sustained load. Plastic deformation occurs when the material does not regain its initial shape after the applied load is removed. Elastic deformation occurs when the material regains its initial shape after the applied load is removed.

When a body is pulled by two equal and opposite forces, resulting in an increase in its length, it experiences tensile stress and strain. On the other hand, when a body is pushed by two equal and opposite forces, resulting in a decrease in its length, it experiences compressive stress and strain.

Compressive stress and compressive strain

Resilience is the ability of a material to absorb energy in the elastic region. It is the total strain energy stored in a given volume of a material within elastic limit. Ductility is the property of a material to be drawn into a wire with the application of tensile force. Toughness is the ability of a material to absorb energy before fracture takes place. Tough materials have the ability to bend, twist or stretch before failure takes place. Therefore, the correct answer is option 2 - Resilience.

Brittle materials fail in torsion at a 45° plane forming an angle with the longitudinal axis due to their weak tensile strength. Ductile materials fail in torsion due to principle shear stress, with the failure plane perpendicular to the longitudinal axis. Brittle materials fail in compression due to shear at a 45° plane from the axis, while ductile materials fail in tension due to shear at a 45° plane forming cup and cone failure. In compression yielding, short compression members fail in compression with a failure plane at 90° to the compressive load.

Along a plane perpendicular to its longitudinal axis

Along the longitudinal direction of the member

Along surface forming 45° angle with the longitudinal axis

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