Determine the state of stress of a beam at the point shown in Figure 2 to represent: a) the principal stresses; b) the maximum in-plane shear stress and the associated average normal stress. c) For each of the two cases mentioned in (a) and (b), determine the corresponding orientation of the element with respect to the original element shown and sketch the results relative to the longitudinal axis of the beam. Please show the full working to provide sufficient information for the sketching to be complete. 15MPa Figure 2 20° 50MPa

Determine the state of stress of a beam at the point shown in Figure 2 to represent: a) the principal stresses; b) the maximum in-plane shear stress and the associated average normal stress. c) For each of the two cases mentioned in (a) and (b), determine the corresponding orientation of the element with respect to the original element shown and sketch the results relative to the longitudinal axis of the beam. Please show the full working to provide sufficient information for the sketching to be complete. 15MPa Figure 2 20° 50MPa

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

(a) Construct Mohr's circle for an element in a uniaxial state of stress (b) Use this Mohr's circle to derive the equation for the normal stress On and shear stress En on the n-face. The equations should depend on Ox and θ (c) Use the Mohr's circle to determine the planes on which the maximum shear stress acts. Sketch a properly oriented maximum-shear-stress element and indicate the normal and shear stresses acting on its faces. Ơn nt o, Note: for (b), the angle θ is between 0 and 90° and is positive
A member is subjected to a major stress of 110 MPa (tensile), minor stress of 40 MPa (tensile) along with a counter clockwise shear stress of 30 MPa. Calculate the Normal stress, tangential stress, Resultant stress and its inclination on plane make 20 to major stress. Validate your analytical results by drawing Mohr’s circle. i) Normal Stress (unit is MPa) = (ii) Tangential Stress (unit is MPa) = ) Resultant Stress (unit is MPa) Resultant inclination (unit in degree) =
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.
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).
For the flat stress state shown in the figure. Use Mohr's circle to determine (show the procedure only with the use of geometry): a. Draw Mohr's circle indicating coordinates of the points that represent the given stress state, center, radius, coordinates of the points that represent the state the maximum and minimum normal stresses, coordinates of the maximum shear and angle of rotation from the stress given to the plane principal. b. Use the results of literal a to draw the element subjected to main forces and the element subjected to maximum shear. 12 MPa 19 MPа y 19 MPа 46 MPа 46 MPа 19 MPа 19 MPа 12 MPa
State of stress at the wall and the roof of the following circular opening bafore the excavation is (a] = |0 4. Find the induced stress components at point a. R W with respect to the given x-y coordinate systerm, and expresst them in the matrix form. b. Find the total stresses at point W, and give them in matrix form. c. Repeat (a) and (b) for the roof. d. Find the stresses oy, Ciy, and tyy at point A which is located at a radial distance twice the radius of the tunnel.
A member is subjected to a major stress of 110 MPa (tensile), minor stress of 40 MPa (compressive) along with a counter clockwise shear stress of 23 MPa. Calculate the Normal stress, tangential stress, Resultant stress and its inclination on plane make 35° to major stress. Validate your analytical results by drawing Mohr's circle. (i) Normal Stress (unit is MPa) = (ii) Tangential Stress (unit is MPa) = (iii) Resultant Stress (unit is MPa) = (iv) Resultant inclination (unit in degree)
find the principal stress , maximum in plane shear stress , average normal stress specdify the orientation of the element in each case , use mohrs circle to solve the question .
At point O of a part subjected to plane stress made of steel material (E = 210 GPa and %3D ww v= 0.3) The tensile components are given below. 240 %3D - 30 MPa *yz yz a) The principal stress components (01, 02 and o3) and their angles with respect to the x-y-z axes of the planes where they are formed calculate b) Calculate the maximum shear stress (tmax) and the angles of the plane in which it is formed with respect to the x-y-z axes. c) Drawthe 2-D and 3-D Mohr circles for the stress components. d) At point O in a section plane passing through point O and having an angle of 30° counterclockwise with the +x-axis Calculate the resulting stress components. e) Calculate the strain components (Exx, EW, Ezz, YXV, YXz and Yyz) and draw the 2-D and 3-D Mohr circles for the strain components.
A member is subjected to a major stress of 115 MPa (tensile), minor stress of 50 MPa (tensile) along with a counter clockwise shear stress of 20 MPa. Calculate the Normal stress, tangential stress, Resultant stress and its inclination on plane make 35° to major stress. Validate your analytical results by drawing Mohr's circle. marks, Mohr's circle - (ENTER ONLY THE VALUES IN THE BOXES BY REFERRING THE UNIT GIVEN IN BRACKET & UPLOAD YOUR HAND WRITTEN ANSWERS IN THE LINK PROVIDED) (i) Normal Stress (unit is MPa) = (ii) Tangential Stress (unit is MPa) (iii) Resultant Stress (unit is MPa) (iv) Resultant inclination (unit in degree) = %3D
Figure shows a beam made from bronze subjected to a 3.5kN.m bending couple and its respective tensile properties. i) With aid of illustration, draw the deformation of the bean and locate the position where the beam experience maximum tensile stress (αmax)t and maximum compressive stress (αmax)c. Accordingly. Determine the magnitude of these two stresses. ii) Sketch the two-dimensional stress distribution acting on point A and point B over the cross-sectional area of the beam as observed from side view. Estimate the magnitude of the stresses at those two points.
Consider the general case of plane stress as shown. Write a computer program that will show a plot of the three Mohr’s circles for the element, and will also determine the maximum in-plane shear stress and the absolute maximumshear stress.