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Figure 1 shows a cantilever beam ABC that is fixed at point A. It is subjected to a uniformly distributed load of 30 kN/m along section AB, a vertical point load of 50 kN and 40 kN at points B and C, respectively, and a clockwise moment of 200 kN. m at point C. The cross-section of the beam is shown in Figure 2. a) Determine the reactions at the support. b) Develop the shear force and bending moment equations for Section AB only. Sketch the shear force and bending moment diagrams and indicate all values at the transition points. d) c) Develop the slope and deflection functions using Macaulay's method. Calculate the maximum bending stresses (both tensile and compressive). f) e) Sketch the bending stress profile. g) h) Calculate the maximum transverse shear stress. At the location of maximum shear force, calculate the transverse shear stress values at the top (point D) and bottom (point E) of the hollow circle. i) Sketch the transverse shear stress profile and indicate all values at the transition points.

Figure 1 shows a cantilever beam ABC that is fixed at point A. It is subjected to a uniformly distributed load of 30 kN/m along section AB, a vertical point load of 50 kN and 40 kN at points B and C, respectively, and a clockwise moment of 200 kN. m at point C. The cross-section of the beam is shown in Figure 2. a) Determine the reactions at the support. b) Develop the shear force and bending moment equations for Section AB only. Sketch the shear force and bending moment diagrams and indicate all values at the transition points. d) c) Develop the slope and deflection functions using Macaulay's method. Calculate the maximum bending stresses (both tensile and compressive). f) e) Sketch the bending stress profile. g) h) Calculate the maximum transverse shear stress. At the location of maximum shear force, calculate the transverse shear stress values at the top (point D) and bottom (point E) of the hollow circle. i) Sketch the transverse shear stress profile and indicate all values at the transition points.

Elements Of Electromagnetics
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
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Figure 1 shows a cantilever beam ABC that is fixed at point A. It is subjected to a uniformly distributed load of 30 kN/m along section AB, a vertical point load of 50 kN and 40 kN at points B and C, respectively, and a clockwise moment of 200 kN. m at point C. The cross-section of the beam is shown in Figure 2. a) Determine the reactions at the support. b) Develop the shear force and bending moment equations for Section AB only. c) Sketch the shear force and bending moment diagrams and indicate all values at the transition points. Develop the slope and deflection functions using Macaulay's method. d) Calculate the maximum bending stresses (both tensile and compressive). f) e) Sketch the bending stress profile. Calculate the maximum transverse shear stress. g) At the location of maximum shear force, calculate the transverse shear stress values h) at the top (point D) and bottom (point E) of the hollow circle. i) Sketch the transverse shear stress profile and indicate all values at the transition points. 2 50 kN 40 kN 30 kN/m 200 KN•M 1.8 m- -1.2 m- Figure 1 125 mm 50 mm 125 mm 150 mm Figure 2
Transcribed Image Text:Figure 1 shows a cantilever beam ABC that is fixed at point A. It is subjected to a uniformly distributed load of 30 kN/m along section AB, a vertical point load of 50 kN and 40 kN at points B and C, respectively, and a clockwise moment of 200 kN. m at point C. The cross-section of the beam is shown in Figure 2. a) Determine the reactions at the support. b) Develop the shear force and bending moment equations for Section AB only. c) Sketch the shear force and bending moment diagrams and indicate all values at the transition points. Develop the slope and deflection functions using Macaulay's method. d) Calculate the maximum bending stresses (both tensile and compressive). f) e) Sketch the bending stress profile. Calculate the maximum transverse shear stress. g) At the location of maximum shear force, calculate the transverse shear stress values h) at the top (point D) and bottom (point E) of the hollow circle. i) Sketch the transverse shear stress profile and indicate all values at the transition points. 2 50 kN 40 kN 30 kN/m 200 KN•M 1.8 m- -1.2 m- Figure 1 125 mm 50 mm 125 mm 150 mm Figure 2
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