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.

Test your knowledge on the behavior of materials undergoing deformation and the analysis of forces and moments affecting solid objects in mechanics of deformable bodies. Explore concepts like stress, strain, and material properties along with the relationship between external loads and internal effects on the body.