Dissemination of IT for the Promotion of Materials Science (DoITPoMS)

DoITPoMS Teaching & Learning Packages Bending and Torsion of Beams Questions
Bending and Torsion of Beams AimsBefore you startIntroductionPole-vaultingBending moments and beam curvaturesMaximising the beam stiffnessBeam deflections from applied bending momentsTwisting moments (torques) and torsional stiffnessSpringsPlastic deformation during beam bendingSummaryQuestionsGoing further
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Questions

Quick questions

You should be able to answer these questions without too much difficulty after studying this TLP. If not, then you should go through it again!

  1. How do the axial stresses within a vaulting pole vary with distance from the neutral axis?

    a They are zero at the neutral axis, rising to a tensile maximum at the outer surface, and a compressive maximum at the inner surface.
    b They are zero at the inner surface and rise linearly to a maximum at the outer surface.
    c They reach a maximum at the neutral axis, falling to zero at the outer and inner surfaces.
    d They are constant throughout the section.

  2. It is important to maximise the beam stiffness when attempting to minimise the deflection of a beam (of given mass). Which of the following shapes, all with dimensions such that they have the same cross-sectional area, will have the highest beam stiffness?

    a An I-beam
    b A square section beam
    c A hollow cylindrical beam
    d A circular section beam

  3. In which of the following situations is torsion occurring?

    a A tree bending in the wind.
    b A wire hanging under its own weight.
    c A screwdriver being used to tighten a screw.
    d The wings on an aircraft acting as cantilever beams during flight.

  4. How can the stress distribution in an elastoplastic beam undergoing bending be predicted?

    a The axial strain will vary linearly from the neutral axis to the free surfaces, and so the stress distribution should increase linearly in the same fashion.
    b The axial strain will vary linearly from the neutral axis to the free surfaces, and the stress distribution can be found from this information and the stress-strain curve of the material.
    c The stress distribution cannot be calculated theoretically and must be found by experiment.
    d The beam will be fully plastic and so the stress will be of constant magnitude throughout the section. This stress can be predicted from the Young's modulus and the yield strain of the material.

Deeper questions

The following questions require some thought and reaching the answer may require you to think beyond the contents of this TLP.

  1. Which of the following sectional shapes will give the highest beam stiffness?
    a Hollow tube of outer diameter 15 cm and inner diameter 14 cm
    b I-beam with a central section 11 cm high by 2 cm wide and flanges 2 cm high by 10 cm wide (giving a total height of 15 cm)

  2. A solid rectangular section beam of length, L = 100 cm, height, h = 5 cm and width, w = 1 cm, is loaded under symmetrical 4-point bending, with 1000 N downward forces applied at 40 cm in from both ends of the bar, which is supported at both ends. A deflection of 5 mm is measured at the centre of the beam. Using these data, calculate the Young's modulus of the beam. From your answer, suggest a likely material for the beam.

  3. Calculate the shear modulus, G , of a material supplied in the form of a hollow tube (length 100 cm, outer diameter 5 cm, wall thickness 0.1 cm), given that, when it is subjected to an applied torque of 1000 N m, an angular twist of 0.10 radians is generated.

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