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If the wide-flange beam is subjected to a shear of [tex]V = 30 \, \text{kN}[/tex], determine the shear force resisted by the web of the beam. Set [tex]w = 200 \, \text{mm}[/tex].

Answer :

the shear force resisted by the web of the wide-flange beam is approximately 30,024 N.

To determine the shear force resisted by the web of the wide-flange beam, we first need to calculate the shear stress on the web.
Shear stress = Shear force / Cross-sectional area
The cross-sectional area of the web can be calculated as:
Area = thickness x width
Here, the width of the web (w) is given as 200 mm. We need to find the thickness of the web.
Assuming that the wide-flange beam is a W-shaped beam, we can use the standard dimensions for a W200x27 beam (where 200 is the depth of the beam in mm and 27 is the thickness of the web in mm).
Therefore, the cross-sectional area of the web would be:
Area = 27 x 200 = 5400 mm^2
Now, we can calculate the shear stress on the web as:
Shear stress = 30,000 N / 5400 mm^2 = 5.56 N/mm^2
Finally, we can calculate the shear force resisted by the web using the shear stress and the cross-sectional area of the web:
Shear force = Shear stress x Area

Shear force = 5.56 N/mm^2 x 5400 mm^2 = 30,024 N

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