Answer:
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Explanation:
Fatigue failure occurs under the condition of (a) High elastic stress (b) High corrosivity (c) High stress fluctuations (d) High
1 answer:
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Answer:
1. = 7.161458
in.⁴
= 36.661458
in.⁴
Iₓ = 28.6458 in.⁴
= 138.6548
in.⁴
2. = 114.
in.⁴
= 37.
in.⁴
Iₓ = 457. in.⁴
= 149.
in.⁴
3. The maximum deflection of the beam is 2.55552 inches
Explanation:
1. The height of the beam having a rectangular cross section is h = 2.5 in.
The breadth of the beam, is = 5.5 in.
The moment of inertia of a rectangular beam through its centroid is given as follows;
= b·h³/12 = 5.5 × 2.5³/12 = 1375/192 = 7.161458
= 7.161458
in.⁴
= h·b³/12 = 2.5 × 5.5³/12 = 6655/192 = 36.661458
= 36.661458
in.⁴
The moment of inertia about the base is given as follows;
Iₓ = b·h³/3 = 5.5 × 2.5³/3 = 625/24 = 28.6458
Iₓ = 28.6458 in.⁴
= h·b³/3 = 2.5 × 5.5³/3 = 6655/48= 138.6548
= 138.6548
in.⁴
2. The height of the beam having a rectangular cross section is h = 7 in.
The breadth of the beam, b = 4 in.
The moment of inertia of a rectangular beam through its centroid is given as follows;
= b·h³/12 = 4 × 7³/12 = 114.
= 114.
in.⁴
= h·b³/12 = 7 × 4³/12 = 37.
= 37.
in.⁴
The moment of inertia about the base is given as follows;
Iₓ = b·h³/3 = 4 × 7³/3 = 457.
Iₓ = 457. in.⁴
= h·b³/3 = 2.5 × 5.5³/3 = 149.
= 149.
in.⁴
3. The deflection, , of a simply supported beam having a point load at the center is given as follows;
The given parameters of the beam are;
The length of the beam, L = 22 ft. = 264 in.
The applied load at the center, W = 750 lbs
The modulus of elasticity for Cedar = 10,000,000 psi
The height of the wood, h = 3 in.
The breadth of the wood, b = 5 in.
The moment of inertia of the wood, = b·h³/12 = 5 × 3³/12 = 11.25 in.⁴
By plugging in the given values, we have;
The maximum deflection of the beam, = 2.55552 inches
Explanation:
Step1
Factor of safety is the number that is taken for the safe design of any component. It is the ratio of failure stress to the maximum allowable stress for the material.
Step2
It is an important parameter for design of any component. This factor of safety is taken according to the environment condition, type of material, strength, type of component etc.
Step3
Different material has different failure stress. So, ductile material fails under shear force. Ductile material’s FOS is based on yield stress as failure stress as after yield point ductile material tends to yield. Brittle material’s FOS is based on ultimate stress as failure stress.
The expression for factor of safety for ductile material is given as follows:
Here, is yield stress and
is allowable stress.
The expression for factor of safety for brittle material is given as follows:
Here, is ultimate stress and
is allowable stress.