The principal strains represent the maximum and

minimum normal strain at a point.

For the state of strain at a point, the maximum

shear strain is usually associated with an average normal strain.

When the state of strain is represented by the

principal strains, no shear strain acts on the element.

When the state of strain is represented by the

maximum shear strain, no normal strain acts on the element.

89.5

MPa (tensile)

39.4

MPa (tensile)

39.4

MPa (compressive)

89.5

MPa (compressive)

Plane

cross-sections remain plane after bending.

The

length of the longitudinal (neutral) axis remains unchanged.

Cross-sections

remain perpendicular to the longitudinal axis after bending.

In-plane

distortion of the cross-section is significant and cannot be neglected.

The

shear stress is zero at the top and bottom surfaces and is maximum at the

neutral axis, where it equals 1.5 times the average shear stress V/A.

The shear stress is maximum at the top and

bottom surfaces of the beam, where the bending stress is also largest.

The

shear stress is maximum at the neutral axis, but its value is equal to V/A

regardless of the cross-section dimensions.

The

shear stress is uniform across the depth of the section, equal to V/A.

The hollow shaft develops a higher maximum

shear stress than the solid shaft, because removing material from the centre

reduces J.

The

hollow shaft develops a lower maximum shear stress than the solid shaft,

because removing material reduces the cross-sectional area and therefore the

stress.

Both

shafts develop the same maximum shear stress because the outer radius is the

same.

The

solid shaft develops a higher maximum shear stress than the hollow shaft,

because its greater J means the stress is more spread out.

Beam 2 has a larger second moment of area (I). By placing more material far from the neutral axis, the flanges make a large contribution to (I=\int y^2 dA), so the same bending moment produces lower curvature and lower bending stress.

Beam 2 has a higher centroid, so the neutral axis is further from the applied load.

The web of Beam 2 removes material near the neutral axis, where bending stress is highest, directly reducing the maximum bending stress.

Beam 2 has more total area, so there is more material to resist the bending load.

Beam 2 distributes bending stress uniformly across the cross-section, so the peak stress is reduced.

Both negative

Negative ε_yy and positive ε_zz

The

shear stress cannot be compared without knowing the diameter of the bolts

The

four-bolt joint has half the shear stress per bolt compared to the two-bolt

joint

Both

joints have the same shear stress in each bolt because the applied force is the

same

The

two-bolt joint has half the shear stress per bolt compared to the four-bolt

joint