mechanics of materials

What is normal stress?

Force / Area

A bar in tension is considered what sign?

Positive stress

What does the variable A represent in the formula σ=P/A?

area resisting load

Shear stress in torsion is given by which formula?

τ=Tr/J

The polar moment of inertia of a solid circular shaft has what units?

m⁴

In bending, which plane has zero strain?

Neutral axis

What does the variable yyy represent in bending σ=My/I

distance from neutral axis

Toughness on a stress-strain curve represents:

Area under entire curve

Ductile materials are identified by:

Large plastic region

Maximum shear stress in a rectangular beam occurs where?

Neutral axis

In the shear formula τ=VQ/It, Q is:

first moment of area

Poisson's ratio is defined as:

B. −εlat/εlong

A point load on a shear diagram causes:

A jump in shear

A distributed load w(x)w(x)w(x) relates to shear by:

dx/dV​=−w

In Mohr's circle, the center is located at:

(σx​+σy​/2​,0)

Principal stresses occur on planes where:

Shear stress is zero

Maximum in-plane shear stress equals:

Radius of Mohr's circle

What is the angle to maximum shear planes?

θp​+45∘

For pure torsion, the stress varies how across the radius?

Linear

The angle of twist formula is:

ϕ=TL/JG

Thermal stress in a constrained bar equals:

EαΔT

In combined loading, the normal stress is:

P/A ​± My/I

The maximum moment in a simply supported beam with a center load occurs:

At midspan

A shoulder fillet increases torsional stress by:

Using a factor Kt

Strain is defined as:

Deformation per original length

The resultant force of a distributed load acts at which location?

Centroid

In the tension vs compression diagram, what is the correct sign convention for stress?

Tension positive, compression negative

The material property that measures the energy absorbed before fracture is:

Toughness

In torsion, the shear strain γ depends on:

Both radius r and angle φ

In a compression test, the true stress is the engineering stress.

Less than

The polar moment of inertia JJJ for a shaft has units of:

m⁴

The angle of twist in a shaft increases when:

Polar moment decreases

Stress concentration factors (Kt) in torsion depend on:

Geometry discontinuities

During heating of a composite bar (Mg + steel), which material carries more load after temperature increase?

Material with higher stiffness (higher E)

In bending, the neutral axis is the location where:

Strain is zero

The moment of inertia (I) of a rectangular cross-section increases most when:

Height increases significantly

The first moment of area Q is:

Zero at centroid

In a wide-flange I-beam, most shear is resisted by the:

Web

Maximum in-plane shear stress is equal to:

Radius of Mohr's circle

On Mohr's circle, principal stresses occur where:

Shear stress is zero

A point load applied to a beam causes what in the shear diagram?

Vertical jump

Shear stress in a rectangular beam is:

Parabolic