d = 100 mmx = 50 MPaFig.01d = 75 mmT = 80 MPa02 Determine the smallest allowable diameter brass rod,of length 3.0m, if the rod is to be twisted through onecomplete revolution without exceeding a shearing stress of50 MPa. For brass, G = 39 GPa.

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Answered: 02 Determine the smallest allowable…

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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An aluminum rod is rigidly attached between a steel rod and a bronze rod as shown below. Axial loads are applied at the positions indicated. Find the maximum value of P in Newton that will not exceed a stress in steel of 150 MPa, in aluminum of 87 MPa, or in bronze of 97 MPa.
Elementary beam theory predicts that the axial bending stress ox in a prismatic beam is given by: ox = (M.I,M,L)y+(M,I.-M.I.) (1,1₂-13/2) where My and M₂ are bending moments applied to a cross-section, and where ly, lz and lyz are second moments of area in the usual notation (Oxyz is a Cartesian coordinate system in which the x axis corresponds to the centroidal axis of the beam). (iii) A Z--section beam has the cross-section shown overleaf (see Figure QB2). The second moments of area of the section about the y and z axes are given as;; ly = 1.12x106mm² and I₂ = 2.87x106 mm4. Show that lyz = 1.35x106 mm² (use the parallel axis theorem). 100 60 10 y -10 10 60 Figure QB2 N (iv) Bending moments Mz = 2.0 kNm and My = 0 kNm act on a cross- -section of the beam of part (iii). Obtain an expression for the bending stress and sketch the orientation of the neutral axis with reference to the y and z axes. What is the maximum tensile value of the axial bending stress and where does it occur?
The solid rod has a diameter of 20mm. Find the following: Angle of twist at C with respect to A (in radians) Angle of twist at B with respect to A (in radians) Maximum shear stress at A (in MPa) (Shear stress at support, at a point 7mm from center. (in MPa) A-36 steel with the following properties: Modulus of Elasticity, E = 29x10^3 ksi or 200 GPa Shear Modulus/Modulus of Rigidity, G = 11.5x10^3 ksi or 79.3 GPa Poisson's Ratio, nu = 0.260 Temperature Coefficient for thermal expansion, a = 6.6x10^-6/°F or 11.7x10^-6/°C

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02 Determine the smallest allowable diameter brass rod, of length 3.0m, if the rod is to be twisted through one complete revolution without exceeding a shearing stress of 60 MPa. For brass, G = 39 GPa.