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 in proportion to the column length.
  • CIt varies inversely with the first power of the column length.
  • DIt varies inversely with the square root of the column length.
  • EIt varies inversely with the fourth 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 with the fifth power of the diameter.
  • BIt increases with the square of the diameter.
  • CIt increases with the third power of the diameter.
  • DIt increases with the fourth power of the diameter.
  • EIt increases linearly with 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. 𝐴𝐵
  2. 𝐶𝐵
  3. 𝐷𝐸
  4. 𝐻𝐹
  5. 𝐹𝐺
  • AII
  • BV
  • CI
  • DIV
  • EIII

Q6:

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

  • AA simple support can provide both support force and moment, whereas a cantilever support can only force at a point.
  • BThey do not differ.
  • CA cantilever support can provide only vertical support, whereas a simple support can only provide transverse support.
  • DA cantilever support can provide both support force and moment, whereas a simple support can only force at a point.
  • 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 increases quadratically from the load end to the cantilevered end.
  • BIt increases linearly from the load end to the cantilevered end.
  • CIt decreases quadratically from the load end to the cantilevered end.
  • DIt is constant.
  • EIt decreases linearly from the load end to the cantilevered end.

Q8:

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

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

Q9:

How do distributed or continuous loads differ from discrete loads?

  • ADiscrete loads occur over a range in space; distributed loads occur at specific locations.
  • BDistributed loads occur over a range in space; discrete loads occur at specific locations.
  • CThere is no real difference.
  • DDiscrete loads may only have values in multiples of 2; distributed loads may have any value.
  • 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?

  • Aend loaded, cantilevered beam
  • Bcenter loaded, simply supported beam
  • Ccenter loaded, cantilevered beam
  • Dsimply supported beam with a distributed load
  • Esimply supported, 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 is zero.
  • BIt decreases linearly from the free end to the supported end.
  • CIt increases quadratically from the free end to the supported end.
  • DIt decreases linearly from the free end to the supported end.
  • EIt is constant.

Q13:

How does column buckling differ from column fracture?

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

Q14:

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

  • ADrawing refers to the strain hardening upon deformation; necking refers to reduction in neck diameter.
  • BNecking refers to the strain hardening upon deformation; drawing refers to reduction in neck diameter.
  • CNecking refers to the reduction in cross sectional area under tension; drawing refers to the introduction of new material into a necked region.
  • 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 a piece of material separating into two or more pieces.
  • CThe process of embrittlement at cold temperatures.
  • DThe process of crack formation during shear flow.
  • EThe process of the creation of many small fragments from one large piece.

Q16:

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

  • Aend loaded, cantilevered beam
  • Bsimply supported beam with a distributed load
  • Cend loaded, simply supported beam
  • Dcenter loaded, simply supported beam
  • Ecenter loaded, cantilevered beam

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 inversely 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 is proportional to the Young’s modulus of the column.
  • EIt does not depend upon the Young’s modulus of the column.

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