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F2 F2 Fig. Q1.a. Complete 3D view Fig. Q1.b. Front view Fig. Q1.c. Cross section Point P is on the inclined plane (i.e., shaded plane) and on the front surface of the beam, which is subjected to external force F. (Fig. Q1.a.). The shaded plane is inclined by angle 0 with respect to negative Z axis (Fig. Q1.b.). The point P is in-plane stress state - stresses in X axis are zero - since point P is on the beam surface. At the point P, a normal vector of the cross-section, of which angle with Z axis is zero, is in parallel with Z axis. The cross-section dimension is shown in Fig. Q1.c. Assumption: Disregard Poisson's effect. Given: F= 50 N; h = 220 mm; w = 900 mm 1. Draw a 2D Mohr's circle (M.C.) - present explicitly radius, center, and principal stresses in the M.C. - by considering only stress components in Y-Z space at point P in Fig. Q1.b. 2. For a case when 0 is 35°, please calculate a normal stress and a shear stress, which occur the shaded plane, at point P. Also, draw the stress states with a square element that has sides in parallel with the inclined plane (Fig. Q1.b.) when 0 is 35° 3. Calculate maximum shear stress at point P using the M.C. drawn in 1); and find an angle 0 of the inclined plane (Fig. Q1.b.) where maximum shear stress occurs

F2 F2 Fig. Q1.a. Complete 3D view Fig. Q1.b. Front view Fig. Q1.c. Cross section Point P is on the inclined plane (i.e., shaded plane) and on the front surface of the beam, which is subjected to external force F. (Fig. Q1.a.). The shaded plane is inclined by angle 0 with respect to negative Z axis (Fig. Q1.b.). The point P is in-plane stress state - stresses in X axis are zero - since point P is on the beam surface. At the point P, a normal vector of the cross-section, of which angle with Z axis is zero, is in parallel with Z axis. The cross-section dimension is shown in Fig. Q1.c. Assumption: Disregard Poisson's effect. Given: F= 50 N; h = 220 mm; w = 900 mm 1. Draw a 2D Mohr's circle (M.C.) - present explicitly radius, center, and principal stresses in the M.C. - by considering only stress components in Y-Z space at point P in Fig. Q1.b. 2. For a case when 0 is 35°, please calculate a normal stress and a shear stress, which occur the shaded plane, at point P. Also, draw the stress states with a square element that has sides in parallel with the inclined plane (Fig. Q1.b.) when 0 is 35° 3. Calculate maximum shear stress at point P using the M.C. drawn in 1); and find an angle 0 of the inclined plane (Fig. Q1.b.) where maximum shear stress occurs

Refrigeration and Air Conditioning Technology (MindTap Course List)
Refrigeration and Air Conditioning Technology (MindTap Course List)
8th Edition
ISBN:9781305578296
Author:John Tomczyk, Eugene Silberstein, Bill Whitman, Bill Johnson
Publisher:John Tomczyk, Eugene Silberstein, Bill Whitman, Bill Johnson
Chapter33: Hydronic Heat
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F2 F2 Fig. Q1.a. Complete 3D view Fig. Q1.b. Front view Fig. Q1.c. Cross section Point P is on the inclined plane (i.e., shaded plane) and on the front surface of the beam, which is subjected to external force F: (Fig. Q1.a.). The shaded plane is inclined by angle e with respect to negative Z axis (Fig. Q1.b.). The point P is in-plane stress state – stresses in X axis are zero - since point P is on the beam surface. At the point P, a normal vector of the cross-section, of which angle with Z axis is zero, is in parallel with Z axis. The cross-section dimension is shown in Fig. Q1.c. Assumption: Disregard Poisson's effect. Given: F = 50 N; h = 220 mm; w = 900 mm 1. Draw a 2D Mohr's circle (M.C.) – present explicitly radius, center, and principal stresses in the M.C. - by considering only stress components in Y-Z space at point P in Fig. Q1.b. - 2. For a case when 0 is 35°, please calculate a normal stress and a shear stress, which occur on the shaded plane, at point P. Also, draw the stress states with a square element that has sides in parallel with the inclined plane (Fig. Q1.b.) when e is 35° 3. Calculate maximum shear stress at point P using the M.C. drawn in 1); and find an angle 0 of the inclined plane (Fig. Q1.b.) where maximum shear stress occurs
Transcribed Image Text:F2 F2 Fig. Q1.a. Complete 3D view Fig. Q1.b. Front view Fig. Q1.c. Cross section Point P is on the inclined plane (i.e., shaded plane) and on the front surface of the beam, which is subjected to external force F: (Fig. Q1.a.). The shaded plane is inclined by angle e with respect to negative Z axis (Fig. Q1.b.). The point P is in-plane stress state – stresses in X axis are zero - since point P is on the beam surface. At the point P, a normal vector of the cross-section, of which angle with Z axis is zero, is in parallel with Z axis. The cross-section dimension is shown in Fig. Q1.c. Assumption: Disregard Poisson's effect. Given: F = 50 N; h = 220 mm; w = 900 mm 1. Draw a 2D Mohr's circle (M.C.) – present explicitly radius, center, and principal stresses in the M.C. - by considering only stress components in Y-Z space at point P in Fig. Q1.b. - 2. For a case when 0 is 35°, please calculate a normal stress and a shear stress, which occur on the shaded plane, at point P. Also, draw the stress states with a square element that has sides in parallel with the inclined plane (Fig. Q1.b.) when e is 35° 3. Calculate maximum shear stress at point P using the M.C. drawn in 1); and find an angle 0 of the inclined plane (Fig. Q1.b.) where maximum shear stress occurs
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