Worksheet: Stress and Strain: Loading

In this worksheet, we will practice describing the behaviours of solid objects under various kinds of loading stresses.

Q1:

How does the critical loading force for a long column vary with the length of the column?

  • AIt varies inversely as the square of the length of the column.
  • BIt varies inversely with the fourth power of the column length.
  • CIt varies inversely with the square root of the column length.
  • DIt varies in proportion to the column length.
  • EIt varies inversely with the first power of the column length.

Q2:

How does the critical loading force for a long column vary with the diameter of the column?

  • AIt increases as the square of the diameter.
  • BIt increases as the square of the diameter.
  • CIt increases linearly with diameter.
  • DIt increases as the square of the diameter.
  • EIt increases with the fourth power of the diameter.

Q3:

The strain produced in a rod for different applied tensile loads is shown in the accompanying diagram. The equilibrium length of the rod is 3.0 cm and its equilbirum diameter is 10.0 mm. What is the ultimate tensile stress of the rod’s material?

Q4:

The strain produced in a rod for different applied tensile loads is shown in the accompanying diagram. The equilibrium length of the rod is 5 cm and its equilbirum diameter is 1.0 mm. What is the approximate yield stress of the material?

Q5:

For the loaded crane hook shown in the accompanying diagram, along which plane is the largest stress likely to exist?

  1. 𝐴 𝐵
  2. 𝐶 𝐵
  3. 𝐷 𝐸
  4. 𝐻 𝐹
  5. 𝐹 𝐺
  • AII
  • BIII
  • CV
  • DIV
  • EI

Q6:

How does a cantilever support differ from a simple beam support?

  • AA cantilever support can provide both support force and moment, whereas a simple support can only force at a point.
  • BA simple support can provide both support force and moment, whereas a cantilever support can only force at a point.
  • CThey do not differ.
  • DA cantilever support can provide only vertical support, whereas a simple support can only provide transverse support.
  • EA cantilever support can only provide transverse support, whereas a simple support can provide both vertical and horizontal support.

Q7:

For a uniformly loaded cantilevered beam, how does the bending moment depend upon position along the length of the beam?

  • AIt decreases linearly from the load end to the cantilevered end.
  • BIt decreases quadratically from the load end to the cantilevered end.
  • CIt increases quadratically from the load end to the cantilevered end.
  • DIt increases linearly from the load end to the cantilevered end.
  • EIt is constant.

Q8:

For a uniformly loaded cantilevered beam, how does shear within the beam depend upon position along the length of the beam?

  • AIt increases linearly from the free end to the supported end.
  • BIt is constant.
  • CIt decreases linearly from the free end to the supported end.
  • DIt increases quadratically from the free end to the supported end.
  • EIt is zero.

Q9:

How do distributed or continuous loads differ from discrete loads?

  • AThere is no real difference.
  • BDiscrete loads may only have values in multiples of 2; distributed loads may have any value.
  • CDiscrete loads occur over a range in space; distributed loads occur at specific locations.
  • DDistributed loads occur over a range in space; discrete loads occur at specific locations.
  • EDistributed loads are evenly spaced; discrete loads may occur at any location.

Q10:

The strain produced in a rod for different applied tensile loads is shown in the accompanying diagram. The equilibrium length of the rod is 5 cm and its equilbirum diameter is 3.0 mm. What is the ultimate tensile stress of the rod’s material?

Q11:

How is the beam configuration shown in the accompanying diagram loaded and supported?

  • Acenter loaded, simply supported beam
  • Bsimply supported, cantilevered beam
  • Csimply supported beam with a distributed load
  • Dend loaded, cantilevered beam
  • Ecenter loaded, cantilevered beam

Q12:

For an end-loaded cantilevered beam, how does shear within the beam depend upon position along the length of the beam?

  • AIt decreases linearly from the free end to the supported end.
  • BIt is constant.
  • CIt is zero.
  • DIt increases quadratically from the free end to the supported end.
  • EIt decreases linearly from the free end to the supported end.

Q13:

How does column buckling differ from column fracture?

  • AColumn buckling is the bending of a column under load; fracture is column breakup.
  • BFracture entails vertical cracks; buckling entails horizontal failure.
  • CColumn buckling and column fracture are the same.
  • DBuckling occurs when the footing of a column collapses; fracture occurs when the column itself breaks up.
  • EColumn fracture is bending under load; buckling is complete collapse.

Q14:

What is the most basic difference between the processes of necking and drawing?

  • ANecking refers to the reduction in cross sectional area under tension; drawing refers to the introduction of new material into a necked region.
  • BDrawing refers to the strain hardening upon deformation; necking refers to reduction in neck diameter.
  • CNecking refers to the strain hardening upon deformation; drawing refers to reduction in neck diameter.
  • DThey are synonymous.
  • EDrawing refers to the reduction in cross-sectional area under tension; necking refers to the introduction of new material into a drawn region.

Q15:

What is the process of fracture as used in the study of the strength of materials?

  • AThe growth of defects.
  • BThe process of the creation of many small fragments from one large piece.
  • CThe process of embrittlement at cold temperatures.
  • DThe process of a piece of material separating into two or more pieces.
  • EThe process of crack formation during shear flow.

Q16:

How is the beam configuration shown in the accompanying diagram loaded and supported?

  • Acenter loaded, cantilevered beam
  • Bcenter loaded, simply supported beam
  • Cend loaded, cantilevered beam
  • Dsimply supported beam with a distributed load
  • Esimply supported beam with a distributed load

Q17:

How does the critical loading force for a long column vary with the Young’s modulus of the column material?

  • AIt is inversely proportional to the square root of the Young’s modulus of the column.
  • BIt is proportional to the Young’s modulus of the column.
  • CIt is proportional to the square root of the Young’s modulus of the column.
  • DIt does not depend upon the Young’s modulus of the column.
  • EIt is inversely proportional to the Young’s modulus of the column.

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