A beam of circular cross section is 3000 mm long and is attached at each end to supports which allow rotation of the ends of the beam in the longitudinal vertical plane of symmetry but prevent rotation of the ends in vertical planes perpendicular to the axis of the beam (Fig. P.14.17). The beam supports an offset load of 40 000 N at mid-span. If the material of the beam suffers elastic breakdown in simple tension at a stress of 145 N/mm², calculate the minimum diameter of the beam on the basis of the Tresca and von Mises theories of elastic failure. Ans. 136 mm (Tresca), 135 mm (von Mises).

A beam of circular cross section is 3000 mm long and is attached at each end to supports which allow rotation of the ends of the beam in the longitudinal vertical plane of symmetry but prevent rotation of the ends in vertical planes perpendicular to the axis of the beam (Fig. P.14.17). The beam supports an offset load of 40 000 N at mid-span. If the material of the beam suffers elastic breakdown in simple tension at a stress of 145 N/mm², calculate the minimum diameter of the beam on the basis of the Tresca and von Mises theories of elastic failure. Ans. 136 mm (Tresca), 135 mm (von Mises).

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Pressure and Stress

Question

A beam of circular cross section is 3000 mm long and is attached at each end to supports which
allow rotation of the ends of the beam in the longitudinal vertical plane of symmetry but prevent
rotation of the ends in vertical planes perpendicular to the axis of the beam (Fig. P.14.17). The
beam supports an offset load of 40 000 N at mid-span.
If the material of the beam suffers elastic breakdown in simple tension at a stress of
145 N/mm?, calculate the minimum diameter of the beam on the basis of the Tresca and
von Mises theories of elastic failure.
Ans. 136 mm (Tresca), 135 mm (von Mises).

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