A beam is subjected to equal bending moments of M₂ = 39 kip-ft. The cross-sectional dimensions are b₁ = 7.9 in., d₁ = 1.2 in., b₂ = 0.75 in., d₂ = 5.8 in., b3 = 3.0 in., and d3 = 2.0 in. Determine: (a) the centroid location (measured with respect to the bottom of the cross-section), the moment of inertia about the z axis, and the controlling section modulus about the z axis. (b) the bending stress at point H. Tensile stress is positive, while compressive stress is negative. (c) the bending stress at point K. Tensile stress is positive, while compressive stress is negative. (d) the maximum bending stress produced in the cross section. Tensile stress is positive, while compressive stress is negative. M₂ M₂ -X b₂ H K b₁ y| b3 [d₁ d₂ d3

A beam is subjected to equal bending moments of M₂ = 39 kip-ft. The cross-sectional dimensions are b₁ = 7.9 in., d₁ = 1.2 in., b₂ = 0.75 in., d₂ = 5.8 in., b3 = 3.0 in., and d3 = 2.0 in. Determine: (a) the centroid location (measured with respect to the bottom of the cross-section), the moment of inertia about the z axis, and the controlling section modulus about the z axis. (b) the bending stress at point H. Tensile stress is positive, while compressive stress is negative. (c) the bending stress at point K. Tensile stress is positive, while compressive stress is negative. (d) the maximum bending stress produced in the cross section. Tensile stress is positive, while compressive stress is negative. M₂ M₂ -X b₂ H K b₁ y| b3 [d₁ d₂ d3

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Combined Loading

Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial forces, torsion, and so on, then such body is said to be under combined loading. A very practical example of combined loading is the crankshaft of an internal combustion engine (IC engine). The crankshaft of the IC engine is under high rpm, which is caused due to the torsional forces. Due to the presence of piston, counterbalances, and internal imbalances, the crankshaft experiences lateral forces and due to the rise in temperature, the crankshaft undergoes thermal expansion, which pulls the crankshaft along the axial direction and lateral direction. The presence of unbalanced loads along the periphery of the crankshaft also induces a bending moment.

Question

A beam is subjected to equal bending moments of M₂ = 39 kip-ft. The cross-sectional dimensions are b₁ = 7.9 in., d₁ = 1.2 in., b₂ = 0.75
in., d₂ = 5.8 in., b3 = 3.0 in., and d3 = 2.0 in. Determine:
(a) the centroid location (measured with respect to the bottom of the cross-section), the moment of inertia about the z axis, and the
controlling section modulus about the z axis.
(b) the bending stress at point H. Tensile stress is positive, while compressive stress is negative.
(c) the bending stress at point K. Tensile stress is positive, while compressive stress is negative.
(d) the maximum bending stress produced in the cross section. Tensile stress is positive, while compressive stress is negative.
M₂
Answer:
(a) y= i
¹₂= i
S=
(b) σH = i
(c) OK= i
(d) Omax
i
N
in.
in.4
on.3
ksi
ksi
ksi
M₂
b₂
H
K
b₁
y|
b3
id₁
d₂
d3

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