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Strength of Materials Sheet 9

  • 1) Question.

    Three hinged arch is

    Answer.
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  • 2) Question.

    If a three hinged parabolic arch carries a uniformly distributed load over the entire span, then any section of the arch is subjected to

    Answer.
    When a three-hinged parabolic arch carries a uniformly distributed load (UDL) over its entire span, any section of the arch is subjected to normal thrust only. Bending moment and shear force are zero throughout the arch under these specific loading conditions. 
    This occurs because:
      • A parabolic shape is the ideal funicular curve for a UDL. This means that the arch's centerline perfectly aligns with the line of thrust—the path that the compressive forces take to resist the load.
      • Horizontal thrust counteracts bending moment. The horizontal thrust generated at the supports creates an internal moment that perfectly balances the bending moment from the vertical UDL, resulting in a net bending moment of zero at every section.

     

    • Zero bending moment leads to zero shear force. Shear force is related to the rate of change of the bending moment. Since the bending moment is zero everywhere, the shear force is also zero throughout the arch. 

     

     

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  • 3) Question.

    In a three hinged arch, the linear and the actual arch meet at

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  • 4) Question.

    Due to rise in temperature in a three hinged arch, induced stress is

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  • 5) Question.

    According to Eddy's theorem, the vertical intercept between the linear arch and the centre line of actual arch at any point represents to some acale

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  • 6) Question.

    The effect of arching a beam is

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  • 7) Question.

    Effective length of a column fixed at one end and hinged at the other end is

    where l is the actual length of the column.

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  • 8) Question.

    Slenderness ratio of a 5 m long column hinged at both ends and having a circular cross-section with diameter 160 mm is

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  • 9) Question.

    Rankine's formula for column is valid when slenderness ratio

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  • 10) Question.

    effective length of a chimmey of 20 m height is taken as

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