-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.
5.10-2 Dimensions of cross section: b = 180 mm, v = 12 mm, h = 420 mm,
i = 380 mm, and V = 125 kN.
(a).
To Find:
The moment of inertia and the maximum shear stress in the web.
Answer to Problem 5.10.2P
The maximum shear stress in the web 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/rectangles:
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 5.10.2P
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:
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 the web.
Answer to Problem 5.10.2P
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 5.10.2P
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:
Shear force in the web is
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Chapter 5 Solutions
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- -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. The minimum shear stress rmin in the web. The average shear stress raver (obtained by dividing the shear force by the area of the web) and the ratio i^/t^ The shear force carried in the web and the ratio V^tV. Noie: 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. 5.10-3 Wide-flange shape, W 8 x 28 (see Table F-L Appendix F); V = 10 karrow_forward-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. The minimum shear stress rmin in the web. The average shear stress raver (obtained by dividing the shear force by the area of the web) and the ratio i^/t^ The shear force carried in the web and the ratio V^tV. 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. 5.10-4 Dimensions of cross section: b = 220 mm, f = 12 mm, h = 600 mm, hx= 570 mm, and V = 200 kN.arrow_forward-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. The minimum shear stress rmin in the web. The average shear stress raver (obtained by dividing the shear force by the area of the web) and the ratio i^/t^. The shear force i^/t^ carried in the web and the ratio V^tV. 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. 5.10-6 Dimensions of cross section: b = 120 mm, a = 7 mm, h = 350 mm, hx= 330 mm, and K=60kN.arrow_forward
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- A cantilever beam AB having rectangular cross sections with varying width bxand varying height hxis subjected to a uniform load of intensity q (sec figure). If the width varies linearly with x according to the equation hx= bBxiL^ how should the height hxvary as a function of v in order to have a fully stressed beam? (Express hxin terms of the height hBat the fixed end of the beam.)arrow_forwardA wood beam reinforced by an aluminum channel section is shown in the figure. The beam has a cross section of dimensions 150 mm x 250 mm, and the channel has a uniform thickness of 6.5 mm. If the allowable stresses in the wood and aluminum are 8 M Pa and 38 M Pa, respectively, and if their moduli of elasticity are in the ratio 1 to 6, what is the maximum allowable bending moment for the beam?arrow_forwardA reinforced concrete slab (see figure) is reinforced with 13-mm bars spaced 160 mm apart at d = 105 mm from the top of the slab. The modulus of elasticity for the concrete is Ec= 25 GPa, while that of the steel is £s = 200 G Pa. Assume that allowable stresses for concrete and steel arecrac = 9.2 MPa and us = 135 MPa. l()5 mm Find the maximum permissible positive bending moment for a l-m wide strip of the slab. What is the required area of steel reinforcement, A^ if a balanced condition must be achieved? What is the allowable positive bending moment? (Recall that in a balanced design, both steel and concrete reach allowable stress values simultaneously under the design moment.)arrow_forward
- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning