Answered: 4.17. Determine the components of…

4.17. Determine the components of stress from the results obtained in (a) v=rsin 0, ve = 2r cos 0 (b) VT = cos 0, 1/4 = 0 (c) v = V₁ = 0 (d) v = (1 - 4) cos 0, Ve= - - (1 + 4/4) sin 0 - B

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter8: Applications Of Plane Stress (pressure Vessels, Beams, And Combined Loadings)

Section: Chapter Questions

Problem 8.4.22P: , Solve the preceding problem using the numerical data: /) = 90mm, h = 280 mm, d = 210 mm, q = 14...

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Problem 4.1
Problem 1: A state of plane stress at a point on the surface of a structure consists of the following stress components: Ox = 25 ksi, oy = 12 ksi, and Txy = 10 ksi. Note that the stress components act in the directions shown on the element below. Ox Txy 12 ksi 5 25 ksi 10 ksi (a) Draw a complete Mohr's circle for this stress state. Clearly label the X and Y faces, the center C, and the radius R. (b) Using Mohr's circle, determine the principal stresses, the maximum in-plane shear stress, and the normal stress that acts on the maximum shear stress plane. Label all of these quantities on the circle. (c) Calculate the orientation of the principal planes and the planes of maximum shear stress. Label all of these quantities on the circle. (d) Show all stresses from part (b) on properly oriented stress element(s). Be sure to include all stress components acting on the elements(s).
The uniform 300-1b bar AB carries a 500-lb vertical force at A. The bar is supported by a pin at B and the 0.5-in. diameter cable CD. Find the stress in the cable. DRAW THE FREE BODY DIAGRAM.
Problem 2: A state of plane stress at a point on the surface of a structure consists of the following stress components: Ox = 18 ksi, oy = 24 ksi, and Txy = 15 ksi. Note that the stress components act in the directions shown on the element below. Ox Txy 24 ksi бу 18 ksi 15 ksi (a) Draw a complete Mohr's circle for this stress state. Clearly label the X and Y faces, the center C, and the radius R. (b) Using Mohr's circle, determine the stress components Ox, Oy, and Txy on an element rotated 25° counter-clockwise from the original element shown. Label all of these quantities on the circle. (c) Show all stresses from part (b) on a properly oriented stress element. Be sure to include all stress components acting on the element.
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3.12 The stress matrix referred to axes Px,x,x3 is given in ksi by 14 21 [o,]- 0 21 21 Let rotated axes Px,x,x, be defined with respect to axes Px,x,x3 by the table of base vectors ê, ê, 2/7 3/7 6/7 3/7 -6/7 2/7 6/7 2/7 -3/7 (a) Determine the stress vectors on planes at P perpendicular to the primed axes; determine tei), te2), and tes) in terms of base vectors ê,, ê, , and ê, .
Determine the state of stress at point A of the rectangular post shown loaded with concentrated forces directed along the y axis equal to 75kN and along the x axis equal to 15kN. 1)Determine the total normal stress along the x and y axes at point A (include if tensile or compressive in your final solutions) 75 kN 50 mm 200 mm- 150 mm OAx= 15 kN OAy= 2) Draw the state of stress of point A 800 mm A 50 mm
The principal strains at a point on the aluminum surface of a tank are P1 = 630(10-6) and P2 = 350(10-6). If this is a case of plane stress, determine the associated principal stresses at the point in the same plane. Eal = 10(103) ksi,nal = 0.33.
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Given the beam and the external loading shown below, if L = 15 m, w1 = 510 N/m and w2 = 1,600 N/m, calculate: • the magnitude and location of the equivalent resultant force (a single equivalent force, for the whole loading block, NOT two equivalent forces from dividing into rectangular and triangular stress blocks). • the reactions at the beam supports. W2 w, A L Resultant force Fr = 单位 (tolerance 1 N, magnitude only) Location xbar = 单位 (tolerance 0.1 m, measured from A) Reactions: Ay = 数字单位 (tolerance 1 N, observe up positive sign convention) MA= 数字单位 (tolerance 10 N*m, observe anti-clockwise positive sign convention)
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Problem 2: For the plane stress state listed below, draw a Mohr's circle diagram properly labeled. Keep in mind that the principal stress is that stress state where the shear stress is zero. That means it is the stress state along the normal stress line in Mohr's space. So, use your Mohr's circle to find the principal normal and shear stresses, and determine the angle from the x axis to o1. 0x = 20 kpsi, oy =-10 kpsi, Txy = 8 kpsi cw