Mechanics of Deformable Bodies Quiz

Modulus of Toughness

• Modulus of toughness is the work done on a unit volume of material as the force is gradually increased from zero to rupture strength, in N.m/m³.
• Toughness is a material's ability to absorb energy without causing it to break.

Elastic and Plastic Ranges

• Elastic range: region from zero to the proportional limit.
• Plastic range: region from plastic limit to rupture strength.

Working Stress, Allowable Stress, and Factor of Safety

• Working stress: actual stress of a material under a given loading.
• Allowable stress: maximum safe stress that a material can carry.
• Factor of safety: ratio of ultimate or yield strength to the allowable strength.

Strain

• Strain is the ratio of the change in length caused by the applied force, to the original length.
• Normal strain (ε): characterizes dimensional changes.
• Shear strain: describes distortion (changes in angle).

Axial Deformation

• Axial deformation: change in length experienced by a structural member along its longitudinal axis due to applied axial loads or forces.
• Types of axial deformation:
  • Elongation: due to tensile force (positive deformation).
  • Contraction: due to compressive force (negative deformation).

Stress in Thin-Walled Sphere and Longitudinal Stress

• Stress in thin-walled sphere: consider a spherical tank subjected to an internal pressure.
• Longitudinal stress: consider the equilibrium of a section cut by a transverse plane on the same tank with internal diameter and wall thickness subjected to an internal pressure.

Proportional Limit (Hooke's Law)

• Hooke's Law: "within the proportional limit, the stress is directly proportional to strain".
• Modulus of Elasticity (E) or Young's Modulus: constant of proportionality "k".

Elastic Limit, Yield Point, Ultimate Strength, and Rupture Strength

• Elastic limit: limit beyond which the material will no longer go back to its original shape when the load is removed.
• Yield point: point at which the material will have an appreciable elongation or yielding without any increase in load.
• Ultimate strength: maximum ordinate in the stress-strain curve, also known as tensile strength.
• Rupture strength: strength of the material at fracture or breaking point.

Modulus of Resilience

• Modulus of resilience: work done on a unit volume of material as the force is gradually increased from zero to proportional limit, in N.m/m³.
• Resilience: ability to absorb energy without creating permanent distortion.

Torsion and Torsional Shearing Stress

• Torsion: loads that create a twist in the members.
• Torsional shearing stress: occurs when a material is subjected to twisting forces, leading to shear stress along its cross-section.

Angle of Twist, Polar Moment of Inertia, Torsional Rigidity, and Torsional Stiffness

• Angle of twist (θ): angle through which the bar length "L" will twist.
• Polar moment of inertia: measure of an object's capacity to oppose or resist torsion when some amount of torque is applied to it on a specified axis.
• Torsional rigidity: amount of resistance a cross-section has against torsional deformation.
• Torsional stiffness: torque required for unit twist.

Power Transmitted by the Shaft

• Power transmitted by the shaft: a shaft rotating with a constant angular velocity "w" (in radians per second) is being acted by a twisting moment "T".

Mechanics of Deformable Bodies

• Branch of physics and engineering mechanics that studies the behavior of materials undergoing deformation.
• Involves analyzing how forces and moments affect the shape and motion of solid objects, considering aspects like stress, strain, and material properties.

Types of Stress

• Normal stress: occurs when a member is loaded by an axial force.
• Shear stress: produced whenever the applied loads cause one section of the body to tend to slide past its adjacent section.
• Tangential stress (or circumferential stress): occurs in a tank with internal diameter and wall thickness subjected to an internal pressure.
• Bearing stress: contact pressure between separate bodies, also classified as normal stress.