The cantilever beam shown is subjected to a concentrated load of P. The cross-sectional dimensions of the wide-flange shape are also shown, where bf = 7.00 in., d = 12.5 in., tf = 0.475 in., tw = 0.250 in.(a) Compute the value of Q that is associated with point K, which is located yk = 3.0 in. above the centroid of the wide-flange shape.(b) If the allowable shear stress for the wide-flange shape is τallow= 12 ksi, determine the maximum concentrated load P than can be applied to the cantilever beam. Calculate the cross-sectional area of the top flange (1), the bottom flange (2), and the web (3).Answers:A1 = in.2.,A2 = in.2.,A3 = in.2.Part 2 Determine the location of the y direction centroids of the top flange (1), the bottom flange (2), and the web (3), with respect to the bottom of the cross-section.Answers:y1 = in.,y2 = in.,y3 = in. Part 3Determine the centroid location in the y direction for the cross-section with respect to the bottom of the cross-section.Answer: y¯ = in. Part 4Determine the moment of inertia Ic1 for the top flange (1) about its own centroid y1.Answer: Ic1 = in.4. Part 5Determine the moment of inertia Iz1 for the top flange (1) about the z centroidal axis of the cross-section.Answer: Iz1 = in.4. Part 6Determine the moment of inertia Ic2 for the bottom flange (2) about its own centroid y2.Answer: Ic2 = in.4. Part 7Determine the moment of inertia Iz2 for the bottom flange (2) about the z centroidal axis of the cross-section.Answer: Iz2 = in.4.Part 8Determine the moment of inertia Iz3 for the web (3) about the z centroidal axis of the cross-section. Note that the centroid of the web is also the centroid of the cross-section.Answer: Iz3 = in.4.Part 9Determine the moment of inertia Iz for the cross-section about the z centroidal axis.Answer: Iz = in.4. Part 10Compute the value of the first moment of area Q that is associated with point K, which is located d = 3.0 in. above the centroid of the wide-flange shape.Answer: QK = in.3. Part 11Determine the maximum value of the first moment of area Q for the cross-section.Answer: Qmax = in.3. Part 12 If the allowable shear stress for the wide-flange shape is τallow= 12 ksi, determine the maximum concentrated load P than can be applied to the cantilever beam.Answer: Pmax = kips. byyPtwKУкdYHH

Answered: Calculate the cross-sectional area of…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Part 2

Determine the location of the y direction centroids of the top flange (1), the bottom flange (2), and the web (3), with respect to the bottom of the cross-section.

Answers:

y₁ = in.,
y₂ = in.,
y₃ = in.

Part 3

Determine the centroid location in the y direction for the cross-section with respect to the bottom of the cross-section.

Answer: y¯ = in.

Part 4

Determine the moment of inertia I_c₁ for the top flange (1) about its own centroid y₁.

Answer: I_c₁ = in.⁴.

Part 5

Determine the moment of inertia I_z₁ for the top flange (1) about the z centroidal axis of the cross-section.

Answer: I_z₁ = in.⁴.

Part 6

Determine the moment of inertia I_c₂ for the bottom flange (2) about its own centroid y₂.

Answer: I_c₂ = in.⁴.

Part 7

Determine the moment of inertia I_z₂ for the bottom flange (2) about the z centroidal axis of the cross-section.

Answer: I_z₂ = in.⁴.

Part 8

Determine the moment of inertia I_z₃ for the web (3) about the z centroidal axis of the cross-section. Note that the centroid of the web is also the centroid of the cross-section.

Answer: I_z₃ = in.⁴.

Part 9

Determine the moment of inertia I_z for the cross-section about the z centroidal axis.

Answer: I_z = in.⁴.

Part 10

Compute the value of the first moment of area Q that is associated with point K, which is located d = 3.0 in. above the centroid of the wide-flange shape.

Answer: Q_K = in.³.

Part 11 Determine the maximum value of the first moment of area Q for the cross-section.

Answer: Q_max = in.³.

Part 12

If the allowable shear stress for the wide-flange shape is τallow= 12 ksi, determine the maximum concentrated load P than can be applied to the cantilever beam.

Answer: P_max = kips.

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