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A beam of T-section has I = 1000 cm4 and depth 10 cm. Flange of the section is in tension. If the maximum tensile stress is two times the maximum compressive stress, what is section modulus in compression?
- a)150 cm3
- b)200 cm3
- c)100 cm3
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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A beam of T-section has I = 1000 cm4 and depth 10 cm. Flange of the s...
= 150 cm3
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A beam of T-section has I = 1000 cm4 and depth 10 cm. Flange of the s...
Given data:
I = 1000 cm4
Depth of section = 10 cm
Maximum tensile stress = 2 * Maximum compressive stress
We need to find the section modulus in compression.
Formula:
Section modulus (Z) = I / y
Where y is the distance from the neutral axis to the extreme fiber.
Calculation:
Let the maximum compressive stress be σc and the maximum tensile stress be σt.
From the given condition, we have:
σt = 2 * σc
Maximum bending stress (σ) = Mc / I * y
Where M is the bending moment.
For the maximum bending stress, we have:
σ = σc + σt / 2
Substituting the values of σt and σc, we get:
σ = 1.5σc
σc = σ / 1.5
Now, for the flange in compression, the maximum compressive stress occurs at the extreme fiber, which is at a distance of 5 cm from the neutral axis.
y = 5 cm
Substituting the values of y and I in the formula for section modulus, we get:
Z = I / y
Z = 1000 cm4 / 5 cm
Z = 200 cm3
Therefore, the section modulus in compression is 200 cm3.
The correct answer is option A.
I = 1000 cm4
Depth of section = 10 cm
Maximum tensile stress = 2 * Maximum compressive stress
We need to find the section modulus in compression.
Formula:
Section modulus (Z) = I / y
Where y is the distance from the neutral axis to the extreme fiber.
Calculation:
Let the maximum compressive stress be σc and the maximum tensile stress be σt.
From the given condition, we have:
σt = 2 * σc
Maximum bending stress (σ) = Mc / I * y
Where M is the bending moment.
For the maximum bending stress, we have:
σ = σc + σt / 2
Substituting the values of σt and σc, we get:
σ = 1.5σc
σc = σ / 1.5
Now, for the flange in compression, the maximum compressive stress occurs at the extreme fiber, which is at a distance of 5 cm from the neutral axis.
y = 5 cm
Substituting the values of y and I in the formula for section modulus, we get:
Z = I / y
Z = 1000 cm4 / 5 cm
Z = 200 cm3
Therefore, the section modulus in compression is 200 cm3.
The correct answer is option A.
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A beam of T-section has I = 1000 cm4 and depth 10 cm. Flange of the section is in tension. If the maximum tensile stress is two times the maximum compressive stress, what is section modulus in compression?a) 150 cm3b) 200 cm3 c) 100 cm3d) None of theseCorrect answer is option 'A'. Can you explain this answer?
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