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A cantilever beam with a 'T' shaped cross-section is loaded with a distributed load as shown below. The intensity of the distributed load is 100N/mm. b = 6.25mm and c=6.25mm. A y Parameter L a d 0 L B 777 Description Beam length T Width of the flange Height of the web Yield stress |←0 →| Value 250 80 75 250 y Units mm mm mm MPa You are tasked with ensuring the beam can withstand the applied loading. To do this you must: a) Calculate the centroid for the given cross-section. Your value of y should be measured from the bottom of the section. Determine an expression for Q (statical moment of area) for the given shape. The expression(s) for Q should be in terms of the variable, y, measured from the bottom of the section.

A cantilever beam with a 'T' shaped cross-section is loaded with a distributed load as shown below. The intensity of the distributed load is 100N/mm. b = 6.25mm and c=6.25mm. A y Parameter L a d 0 L B 777 Description Beam length T Width of the flange Height of the web Yield stress |←0 →| Value 250 80 75 250 y Units mm mm mm MPa You are tasked with ensuring the beam can withstand the applied loading. To do this you must: a) Calculate the centroid for the given cross-section. Your value of y should be measured from the bottom of the section. Determine an expression for Q (statical moment of area) for the given shape. The expression(s) for Q should be in terms of the variable, y, measured from the bottom of the section.

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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A cantilever beam with a 'T' shaped cross-section is loaded with a distributed load as shown below. The intensity of the distributed load is 100N/mm. b = 6.25mm and c=6.25mm. A y Parameter L a d 0 L B 777 Description Beam length T Width of the flange Height of the web Yield stress |←0 →| Value 250 80 75 250 y Units mm mm mm MPa You are tasked with ensuring the beam can withstand the applied loading. To do this you must: a) Calculate the centroid for the given cross-section. Your value of y should be measured from the bottom of the section. Determine an expression for Q (statical moment of area) for the given shape. The expression(s) for Q should be in terms of the variable, y, measured from the bottom of the section.
Transcribed Image Text:A cantilever beam with a 'T' shaped cross-section is loaded with a distributed load as shown below. The intensity of the distributed load is 100N/mm. b = 6.25mm and c=6.25mm. A y Parameter L a d 0 L B 777 Description Beam length T Width of the flange Height of the web Yield stress |←0 →| Value 250 80 75 250 y Units mm mm mm MPa You are tasked with ensuring the beam can withstand the applied loading. To do this you must: a) Calculate the centroid for the given cross-section. Your value of y should be measured from the bottom of the section. Determine an expression for Q (statical moment of area) for the given shape. The expression(s) for Q should be in terms of the variable, y, measured from the bottom of the section.
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Follow-up Question
Create a 2D contour plot to allow the performance of the structure to be assessed against the maximum distortion energy (von Mises) criteria. Comment on the results. You can do this by plotting a contour of the von-mises stress and then normalising the result against the yield stress. This will produce a contour plot of the failure index. This index represents the ratio of the von-mises stress to the yield stress of the material.
Transcribed Image Text:Create a 2D contour plot to allow the performance of the structure to be assessed against the maximum distortion energy (von Mises) criteria. Comment on the results. You can do this by plotting a contour of the von-mises stress and then normalising the result against the yield stress. This will produce a contour plot of the failure index. This index represents the ratio of the von-mises stress to the yield stress of the material.
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Follow-up Question
Create a two-dimensional contour plot of the bending and transverse shear stresses over the length and height of the beam (xy plane). You can use your results above to validate your approach. Note: it is more convenient to perform these calculations in a program such as Matlab or Python. Please make sure that you upload your script (.m or .py files) to the unit site (along with your assignment).
Transcribed Image Text:Create a two-dimensional contour plot of the bending and transverse shear stresses over the length and height of the beam (xy plane). You can use your results above to validate your approach. Note: it is more convenient to perform these calculations in a program such as Matlab or Python. Please make sure that you upload your script (.m or .py files) to the unit site (along with your assignment).
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Follow-up Question
Create a graph of the shear and bending stresses at the fixed support (B) over the cross- section. The stresses should be plotted as a function of y, measured from the bottom of the section. NOTE: this is a simplified calculation and you do not need to account for the additional stress caused by the sharp corner (stress concentration). You should calculate the stresses using the bending and shear formulas.
Transcribed Image Text:Create a graph of the shear and bending stresses at the fixed support (B) over the cross- section. The stresses should be plotted as a function of y, measured from the bottom of the section. NOTE: this is a simplified calculation and you do not need to account for the additional stress caused by the sharp corner (stress concentration). You should calculate the stresses using the bending and shear formulas.
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