Answer :
Final answer:
To find the radius of curvature, use the formula R = (E * h^2) / (6 * M0). To find the maximum slope, use the formula slope = (M0 * h) / (2 * E). To find the maximum deflection, use the formula deflection = (5 * M0 * h^4) / (384 * E).
Explanation:
To determine the radius of curvature of the beam, we can use the formula:
R = (E * h^2) / (6 * M0)
where R is the radius of curvature, E is the Young's modulus, h is the depth of the beam, and M0 is the moment.
In this case, R = (29000 ksi * (10 in)^2) / (6 * M0)
To find the maximum slope, we can use the formula:
slope = (M0 * h) / (2 * E)
where slope is the maximum slope, M0 is the moment, h is the depth of the beam, and E is the Young's modulus.
Finally, to find the maximum deflection, we can use the formula:
deflection = (5 * M0 * h^4) / (384 * E)
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Final answer:
The radius of curvature of the beam can be calculated using the formula R = M/3.6, where R is the radius of curvature and M is the moment. The maximum slope of the beam can be calculated using the formula θmax = (M * L)/(2 * E * I), where θmax is the maximum slope, M is the moment, L is the length of the beam, E is the Young's modulus, and I is the moment of inertia. The maximum deflection of the beam can be calculated using the formula δmax = (M * L^2)/(6 * E * I), where δmax is the maximum deflection.
Explanation:
To determine the radius of curvature of the beam, we can use the formula for the stress at the outer fibers of a beam under constant moment:
σ = My/I
where σ is the stress, M is the moment, y is the distance from the neutral axis to the outer fiber, and I is the moment of inertia. Rearranging the formula to solve for the radius of curvature, we have:
R = (My)/(σY)
where R is the radius of curvature and σY is the yield stress of the material. Substituting the given values, we have:
R = (M * 10)/(36)
R = M/3.6
The beam's maximum slope can be calculated using the formula:
θmax = (M * L)/(2 * E * I)
where θmax is the maximum slope, L is the length of the beam, and E is the Young's modulus of the material. The beam's maximum deflection can be calculated using the formula:
δmax = (M * L^2)/(6 * E * I)
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