-1 through 5.10-6 A wide-flange beam (see figure) is subjected to a shear force V. Using the dimensions of the cross section, calculate the moment of inertia and then determine the following quantities:
- The maximum shear stress tinixin the web.
Note: Disregard the fillets at the junctions of the web and flanges and determine all quantities, including the moment of inertia, by considering the cross section to consist of three rectangles.
5.10-1 Dimensions of cross section: b = 6 in,, ï = 0.5 in., h = 12 in,, A, = 10.5 in., and V = 30 k.
(a).
To Find:
The moment of inertia and the maximum shear stress in the web.
Answer to Problem 5.10.1P
The maximum shear stress is
Explanation of Solution
Given Information:
Shear Force
Dimensions,
Concept Used:
Following formula will be used
Maximum shear stress,
Moment of inertia of rectangle,
Calculation:
Area of upper and lower flanges,
Total area of cross section:
Second rectangle is
In which
The first moment of areas of
By putting the values of
The moment of inertia for the I section is given by following formula:
The maximum value of shear stress will be at neutral axis when
Conclusion:
The maximum shear stress in the web is
(b).
To Find:
The minimum shear stress in web.
Answer to Problem 5.10.1P
The minimum shear stress in the web is =
Explanation of Solution
Given Information:
Shear Force
Dimensions,
Concept Used:
Following formula will be used
Minimum shear stress,
Calculation:
Area of upper and lower flanges:
Total area of cross section:
Second rectangle is
In which
The first moment of areas of
By putting the values of
The moment of inertia for the I section is given by following formula:
The minimum value of shear stress will be at
Conclusion:
The minimum shear stress in the web is
(c).
To Find:
The average shear stress in web.
Answer to Problem 5.10.1P
The average shear stress in the web is =
Explanation of Solution
Given Information:
Shear Force
Dimensions,
Concept Used:
Following formula will be used
Average shear stress,
Calculation:
The average shear stress in the web is:
Conclusion:
The average shear stress in the web is =
(d).
To Find:
Shear force
Answer to Problem 5.10.1P
The shear force in the web is =
Explanation of Solution
Given Information:
Shear Force
Dimensions,
Concept Used:
Following formula will be used:
Shear stress in the web,
Calculation:
Shear stress in the web:
Conclusion:
The shear force in the web is
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