Concept explainers
The composite beam shown is made by welding C200 × 17.1 rolled-steel channels to the flanges of a W250 × 80 wide-flange rolled-steel shape. Knowing that the beam is subjected to a vertical shear of 200 kN, determine (a) the horizontal shearing force per meter at each weld, (b) the shearing stress at point a of the flange of the wide-flange shape.
Fig. p6.97
(a)
The horizontal shearing force per meter at each weld.
Answer to Problem 97RP
The horizontal shearing force per meter at each weld is
Explanation of Solution
Given information:
The composite beam is made by welding
The beam is subjected to a vertical shear of
Calculation:
Provide the section properties of
The Area of the section is
The width of the flange is
The thickness of flange is
The moment of inertia of the section is
The centroid of the section is
Provide the section properties of
The overall depth of the section is
Thickness of flange is
Moment of inertia of the section is
Sketch the channel section above the neutral axis as shown in Figure 1.
Refer to Figure 1.
Calculate the location of the centroid
Calculate the moment of inertia (I) for the composite beam as shown below.
Substitute
Calculate the first moment of area as shown below.
Calculate the first moment for the two welds (Q) as shown below.
Calculate the horizontal shear per unit length (q) as shown below.
Substitute
Calculate the shearing force per meter of weld for one weld as shown below.
Therefore, the horizontal shearing force per meter at each weld is
(b)
The shearing stress at point a of the flange.
Answer to Problem 97RP
The shearing stress at point a of the flange is
Explanation of Solution
Given information:
The beam is subjected to a vertical shear of
Calculation:
Refer to part (a).
The moment of inertia is
Sketch the channel section through point a as shown in Figure 2.
Refer to Figure 2.
The thickness of the section is
Substitute
Calculate the location of the centroid at point a
Calculate the first moment of area
Calculate the shear stress
Substitute
Therefore, the shearing stress at point a of the flange is
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Chapter 6 Solutions
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