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Learning Goal: To calculate the shear stress at a point in the web of an l- beam section subjected to a shear force. When a beam section is subjected to a shear load, a shear stress distribution is developed on the section. The distribution of the shear stress is not linear. Elasticity theory can be used to calculate the shear stress at any point. However, a simpler method can be used to calculate the average shear stress across the width of the section, a distance y above or below the neutral axis. The average VQ shear stress is given by T=. Here Vis the shear It force on the section, I is the moment of inertia of the entire section about the neutral axis, and t is the width of the section at the distance y where the shear stress is being calculated. Q is the product of the area of the section above (or below) y and the distance from the neutral axis to the centroid of that area (Figure 1). In short, Q is the moment of the area about the neutral axis. An I-beam has a flange width b = 400 mm, height h = 400 mm, web thickness t = 13 mm, and flange thickness tƒ = 21 mm. Use the following steps to calculate the shear stress at a point 130 mm above the neutral axis. Part A - Moment of inertia The shear formula includes the moment of inertia of the whole cross section, I, about the neutral axis. Calculate the moment of inertia. Express your answer with appropriate units to three significant figures. ► View Available Hint(s) I = μA Value Submit Part B - Q for the given point H Units μÀ The shear stress 130 mm above the neutral axis depends on the value of Q for the area above that point. Calculate the value of Q. Express your answer with appropriate units to three significant figures. ▸ View Available Hint(s) ?

Learning Goal: To calculate the shear stress at a point in the web of an l- beam section subjected to a shear force. When a beam section is subjected to a shear load, a shear stress distribution is developed on the section. The distribution of the shear stress is not linear. Elasticity theory can be used to calculate the shear stress at any point. However, a simpler method can be used to calculate the average shear stress across the width of the section, a distance y above or below the neutral axis. The average VQ shear stress is given by T=. Here Vis the shear It force on the section, I is the moment of inertia of the entire section about the neutral axis, and t is the width of the section at the distance y where the shear stress is being calculated. Q is the product of the area of the section above (or below) y and the distance from the neutral axis to the centroid of that area (Figure 1). In short, Q is the moment of the area about the neutral axis. An I-beam has a flange width b = 400 mm, height h = 400 mm, web thickness t = 13 mm, and flange thickness tƒ = 21 mm. Use the following steps to calculate the shear stress at a point 130 mm above the neutral axis. Part A - Moment of inertia The shear formula includes the moment of inertia of the whole cross section, I, about the neutral axis. Calculate the moment of inertia. Express your answer with appropriate units to three significant figures. ► View Available Hint(s) I = μA Value Submit Part B - Q for the given point H Units μÀ The shear stress 130 mm above the neutral axis depends on the value of Q for the area above that point. Calculate the value of Q. Express your answer with appropriate units to three significant figures. ▸ View Available Hint(s) ?

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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Learning Goal: To calculate the shear stress at a point in the web of an l- beam section subjected to a shear force. When a beam section is subjected to a shear load, a shear stress distribution is developed on the section. The distribution of the shear stress is not linear. Elasticity theory can be used to calculate the shear stress at any point. However, a simpler method can be used to calculate the average shear stress across the width of the section, a distance y above or below the neutral axis. The average VQ shear stress is given by T = Here V is the shear It force on the section, I is the moment of inertia of the entire section about the neutral axis, and ₺ is the width of the section at the distance y where the shear stress is being calculated. Q is the product of the area of the section above (or below) y and the distance from the neutral axis to the centroid of that area (Figure 1). In short, Qis the moment of the area about the neutral axis. Figure 1 of 1 An I-beam has a flange width b = 400 mm, height h = 400 mm, web thickness tw = 13 mm, and flange thickness tƒ = 21 mm . Use the following steps to calculate the shear stress at a point 130 mm above the neutral axis. Part A - Moment of inertia I = Submit Value The shear formula includes the moment of inertia of the whole cross section, I, about the neutral axis. Calculate the moment of inertia. Express your answer with appropriate units to three significant figures. ► View Available Hint(s) O μA Part B - Q for the given point = 0 μÅ Units Value 上を下 H www ? The shear stress 130 mm above the neutral axis depends on the value of Q for the area above that point. Calculate the value of Q. Express your answer with appropriate units to three significant figures. ► View Available Hint(s) Units b tr ? h
Transcribed Image Text:Learning Goal: To calculate the shear stress at a point in the web of an l- beam section subjected to a shear force. When a beam section is subjected to a shear load, a shear stress distribution is developed on the section. The distribution of the shear stress is not linear. Elasticity theory can be used to calculate the shear stress at any point. However, a simpler method can be used to calculate the average shear stress across the width of the section, a distance y above or below the neutral axis. The average VQ shear stress is given by T = Here V is the shear It force on the section, I is the moment of inertia of the entire section about the neutral axis, and ₺ is the width of the section at the distance y where the shear stress is being calculated. Q is the product of the area of the section above (or below) y and the distance from the neutral axis to the centroid of that area (Figure 1). In short, Qis the moment of the area about the neutral axis. Figure 1 of 1 An I-beam has a flange width b = 400 mm, height h = 400 mm, web thickness tw = 13 mm, and flange thickness tƒ = 21 mm . Use the following steps to calculate the shear stress at a point 130 mm above the neutral axis. Part A - Moment of inertia I = Submit Value The shear formula includes the moment of inertia of the whole cross section, I, about the neutral axis. Calculate the moment of inertia. Express your answer with appropriate units to three significant figures. ► View Available Hint(s) O μA Part B - Q for the given point = 0 μÅ Units Value 上を下 H www ? The shear stress 130 mm above the neutral axis depends on the value of Q for the area above that point. Calculate the value of Q. Express your answer with appropriate units to three significant figures. ► View Available Hint(s) Units b tr ? h
Figure H < 1 of 1 Part C-Shear stress Use the results from Parts A and B to calculate the shear stress at a point 130 mm above the neutral axis if the shear force on the section is V = 5.8 KN. Express your answer with appropriate units to three significant figures. ► View Available Hint(s) T = O μA Value Submit < Return to Assignment Units Provide Feedback ?
Transcribed Image Text:Figure H < 1 of 1 Part C-Shear stress Use the results from Parts A and B to calculate the shear stress at a point 130 mm above the neutral axis if the shear force on the section is V = 5.8 KN. Express your answer with appropriate units to three significant figures. ► View Available Hint(s) T = O μA Value Submit < Return to Assignment Units Provide Feedback ?
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