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Problems

2.1 (A/B). Compare the crippling loads given by the Euler and Rankine-Gordon formulae for a pin-jointed cylindrical strut 1.75 m long and of 50 mm diameter. (For Rankine-Gordon use ay = 315 MN/m2; a = 1/7500; e = 200 GN/m2.) [197.7, 171 kN.]

2.2 (A/B). In an experiment an alloy rod 1 m long and of 6 mm diameter, when tested as a simply supported beam over a length of 750 mm, was found to have a maximum deflection of 5.8 mm under the action of a central load of 5 N.

(a) Find the Euler buckling load when this rod is tested as a strut, pin-jointed and guided at both ends.

(b) What will be the central deflection of this strut when the material reaches a yield stress of 240 MN/m2?

P My

(Clue: maximum stress = — ± — where M = P x dmax ) A I

23 (B) A steel strut is built up of two T-sections riveted back to back to form a cruciform section of overall dimensions 150 mm x 220 mm. The dimensions of each T-section are 150 mm x 15 mm x 110 mm high. The ends of the strut are rigidly secured and its effective length is 7 m. Find the maximum safe load that this strut can carry with a factor of safety of 5, given irv = 315 MN/m2 and a = 1/30000 in the Rankine-Gordon formula.

2A (B). State the assumptions made when deriving the Euler formula for a strut with pin-jointed ends. Derive the Euler crippling load for such a strut-the general equation of bending and also the solution of the differential equation may be assumed.

A straight steel rod 350 mm long and of 6 mm diameter is loaded axially in compression until it buckles. Assuming that the ends are pin-jointed, find the critical load using the Euler formula. Also calculate the maximum central deflection when the material reaches a yield stress of 300 MN/m2 compression. Take E = 200 GN/m2.

2.5 (B). A steel stanchion 5 m long is to be built of two I-section rolled steel joists 200 mm deep and 150 mm wide flanges with a 350 mm wide x 20 mm thick plate riveted to the flanges as shown in Fig. 2.18. Find the spacing of the joists so that for an axially applied load the resistance to buckling may be the same about the axes XX and YY. Find the maximum allowable load for this condition with ends pin-jointed and guided, assuming a = 1/7500 and ctv = 315 MN/m2 in the Rankine formula.

150 mm

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