05-05ChapGere.0010

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Problem 5.12-4 A rigid frame ABC is formed by welding two steel pipes at B (see figure). Each pipe has cross-sectional area A 11.31 10 3 mm 2 , moment of inertia I 46.37 10 6 mm 4 , and outside diameter d 200 mm. Find the maximum tensile and compressive stresses t and c , respectively, in the frame due to the load P 8.0 kN if L H 1.4 m. Solution 5.12-4 Rigid frame SECTION 5.12 Beams with Axial Loads 359 B P A C H d d d L L Load P at midpoint B R EACTIONS : B AR AB : d diameter c d /2 sin H H 2 L 2 tan H L R A R C P 2 A XIAL FORCE : N R A sin sin B ENDING MOMENT : T ENSILE STRESS S UBSTITUTE NUMERICAL VALUES : P 8.0 kN L H 1.4 m 45º sin d 200 mm A 11.31 10 3 mm 2 I 46.37 10 6 mm 4 0.250 MPa 12.08 MPa 11.83 MPa (tension) 12.33 MPa (compression) s c N A Mc I 0.250 MPa 12.08 MPa s t (8.0 kN)(1 2 ) 2(11.31 10 3 mm 2 ) (8.0 kN)(1.4 m)(200 mm) 4(46.37 10 6 mm 4 ) 1 1 2 s t N A

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