Solid Mechanics Final Exam Review

Stress

The intensity of the internal force acting on a specific plane passing through a point.

Normal

_______ stress is the intensity of the force acting perpendicular to the plane.

________ stress is the intensity of the force acting tangent to the plane.

Homogeneous

A term used to describe a material that has the same physical and mechanical properties throughout.

Isotropic

A term used to describe a material that has the same properties in all directions.

Ductile

Any material that can be subjected to large strains before failure.

Brittle

Materials that exhibit little or no yielding before failure.

Strain-Energy Density

The amount of energy required to deform a material.

Modulus of Resilience

The strain-energy density at the proportional limit.

Modulus of Toughness

The maximum amount of energy a material can absorb before fracture. This value is represented by the area under the entire stress-strain diagram.

Clockwise

The sign convention for shear force typically dictates that positive shear should act to rotate the element _______.

Smiley Face

The sign convention for bending moments dictates that a positive moment should act such that the element forms a ___________.

Homogeneous

One limitation of the shear formula is that it only approximates the stress for straight prismatic members made of _________ material.

b/h > 2

One limitation of the shear formula is that it cannot accurately approximate the stress in “short” or “flat” sections (such as where __________)

One limitation of the shear formula is that it should not be used on inclined boundaries.

10

The governing condition for thin-walled pressure vessel analysis is that the radius/thickness ratio must be > _______.

45

Maximum in-plane shear stress acts _______ degrees away from the principal stress orientation.

Isotropic

The orientation corresponding to the principal strains will coincide with the orientation corresponding to the principal stresses if the material is _______.

Creep

Time-dependent permanent deformation. In other words, this property describes the behavior by which a material will continue to deform if it has to support a load for a long period of time.

Rubber Band

An example of creep is seen in _________ which fail to return to their initial state after being held in a stretched position for an extended period of time (such as when wound around a large container).

Creep is also seen in telephone poles as the long-term tension of the electrical lines causes the post to deform.

Fatigue

The behavior of a material in which its internal structure will continuously break down when subjected to repeated cycles of stress or strain.

Materials fail in this way because microscopic imperfections in the material create areas of high localized stress. This eventually leads to the formation of minute cracks that propagate, further increasing the localized stress in such regions.

Largest dimension

According to Saint-Venant’s Principle, the average stress in a member reaches a uniform value when analyzing a point located at a distance equal to __________ relative to the loading. For instance, if a 2×4 wooden board is subjected to tension at one end, the stress only reaches a uniform value 4 inches from the end under load.

Statically Indeterminate

A body is said to be ___________ if it is supported by more reactive forces than needed for equilibrium (such as an axially loaded member positioned between two rigid supports). In other words, there will be more unknowns than equations of equilibrium.

Thermal Stresses

______________ are developed when a statically indeterminate member is subjected to a change in temperature that would cause the material to otherwise expand or contract.

Stress Concentration Factor

Denoted by the variable K, this quantity refers to the ratio of the maximum stress to the average normal stress acting at the cross section of a member. In other words, such factors help determine the maximum stress in regions of localized stress concentration.