1. The state of stress in a machine element with respeet to x-y'axis is shown in Figure 1. The principal angle 0, (-20°) as shown in the figure defines the principal axes x' and y' (Note: orientation of stresses on the element is generic and is not related to the stress tensor). 40 MPa Ty -20 Tay =-20° Oy Figure 1 (a)(i) Draw the reference axes x, y, x', y' showing 0, (ii) Determine the four direction cosines that the principal directions make with the x-y axes. (b)Draw and label Mohr's circle for the state of stress shown identifying the following points on the circle: numerical values of the coordinates of (i) the center (6ave, Txy), (ii) stresses from the given stress tensor (associated with the A and B planes. Note: Mohr's circle can be drawn with only ơ, ɑy ), (iii) the principal angle (0,), (iv) the principal stresses (ơ¡ 02), (v) maximum shear stress (tmax). (c)Determine the shear stress txy. (d)Show the stress tensor (normal and shear stresses) on a properly oriented element. (e)Find (i) the maximum shear stress; and (ii) the orientation of the maximum shear stress plane (means angle). (f) Find the principal stresses ơ1 and ơ2 via a Mohr's circle analysis. o)Sketch the results from (e) on a pronerly oriented element

Q: The state of stress at a point in a member is shown in A 0x' = 60° σ y B on the element. Assume ox…

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Q: Mohr’s circle is shown for a point in a physical object that is subjected to plane stress. Each…

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Q: The rectangular plate is subjected to force P that causes elongation in the horizontal direction and…

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Q: appropriate sketch (e.g., see Figure 12.15 or Figure 12.16).

A: Given:- Each grid square is 740 psi in size. To find:- (a) Determine the stresses σx, σy, and the…

Q: Consider a solid shaft is carrying a torque T and an axial load P as shown in Figure 1) Calculate…

A: radius R=20 cm    and diameter  d=40 cm 400 mmcross section  area   A=π4×4002=0.1256m2 Normal force…

Q: Consider a point in a structural member that is subjected to plane stress. Normal and shear stresses…

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Q: y T C X b

A: From the following mohr circle we can identify the required parameters.

Q: Mohr's circle is shown for a point in a physical object that is subjected to plane stress. Each grid…

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Q: (a) Determine the stresses Ox, Oy, and the magnitude of Txy and show them on a stress element. (b)…

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Q: Mohr's circle is shown for a point in a physical object that is subjected to plane stress. Each grid…

A: Note that the sign convention for shear stress has been taken as ANTICLOCKWISE POSITIVE .   If it…

Q: Mohr's circle is shown for a point in a physical object that is subjected to plane stress. Each grid…

A: (a) σx= 2560 psi σy= -1280 psi txy= 3840 psi (b) σ(P1)= 4960 psi σ(P2)=-3680 psi Tmax = 4320 psi

Solid Mechanics

Engineering mechanics is a branch of science that deals with forces causing bulk motion in bodies and the effect that these forces cause on the bodies. Engineering mechanics does not deal with the internal changes that occur on account of these external forces. The internal effects in a body or a material under the action of external forces are studied in a new branch of science called solid mechanics, the strength of materials, or the mechanical behavior of engineering materials.