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Algebra: a textbook of determinants, matrices, and algebraic by Ferrar W.L. PDF

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By Ferrar W.L.

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15. 14 by use of Mohr’s circle. Ans. 16. A plane element in a body is subject to the stresses σ x = 20 MPa, σ y = 0, and τ xy = 30 MPa. Determine analytically the normal and shearing stresses existing on a plane inclined at 45° to the x-axis. Ans. 17. A plane element is subject to the stresses σ x = 50 MPa, σ y = 50 MPa, and τ xy = 0. Determine analytically the maximum shearing stress existing in the element. Ans. 18. A plane element is subject to the stresses σ x = 60 MPa, σ y = −60 MPa, and τ xy = 0.

A positive normal stress or shear stress on a negative face acts in the negative direction. 35 CHAPTER 3 36 Combined Stresses We shall introduce the N- and T-axes normal and tangential to the inclined plane, as shown. Let t denote the thickness of the element perpendicular to the plane of the page. Let us begin by summing forces in the N-direction. 1) Thus the normal stress s on any plane inclined at an angle q with the x-axis is known as a function of sx, sy, txy, and q. 2) Thus the shearing stress t on any plane inclined at an angle q with the x-axis is known as a function of σ x , σ y , τ xy , and q.

A 100 kW carbon dioxide laser system is employed to form the joint. If the allowable shearing stress in the alloy is 440 MPa and the joint is assumed to be 100 percent efficient, determine the maximum allowable force P that may be applied. Fig. 2-14 SOLUTION: A free-body diagram of the right strip has the form shown in Fig. 2-15. There, s denotes normal stress in the weld on the 45° plane and t the shearing stress. These are, of course, forces per unit area on the 45° (a) (b) Fig. 2-15 CHAPTER 2 Shear Stresses 33 plane and these must be multiplied by the area of the 45° plane which is bt/cos 45°, where t denotes strip thickness and b the width.

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Algebra: a textbook of determinants, matrices, and algebraic forms by Ferrar W.L.


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