Calculate the cross-sectional area of the top flange (1), the bottom flange (2), and the web (3). Answers: A1 = in.2.,
Calculate the cross-sectional area of the top flange (1), the bottom flange (2), and the web (3). Answers: A1 = in.2.,
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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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.
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.
Answer: y¯ = in.
Part 4
Determine the moment of inertia Ic1 for the top flange (1) about its own centroid y1.
Answer: Ic1 = in.4.
Answer: Ic1 = in.4.
Part 5
Determine the moment of inertia Iz1 for the top flange (1) about the z centroidal axis of the cross-section.
Answer: Iz1 = in.4.
Answer: Iz1 = in.4.
Part 6
Determine the moment of inertia Ic2 for the bottom flange (2) about its own centroid y2.
Answer: Ic2 = in.4.
Answer: Ic2 = in.4.
Part 7
Determine the moment of inertia Iz2 for the bottom flange (2) about the z centroidal axis of the cross-section.
Answer: Iz2 = in.4.
Answer: Iz2 = in.4.
Part 8
Determine 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.
Answer: Iz3 = in.4.
Part 9
Determine the moment of inertia Iz for the cross-section about the z centroidal axis.
Answer: Iz = in.4.
Answer: Iz = 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: QK = in.3.
Answer: QK = in.3.
Part 11
Determine 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.
Answer: Pmax = kips.
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