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A short timber post of rectangular section has one side of the section twice the other. when the post loaded with 150kn it contract's by 0.01mm. calculate yhe sectional dimensions of the post?
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A short timber post of rectangular section has one side of the section...
Problem Statement: A short timber post of rectangular section has one side of the section twice the other. When the post loaded with 150kN it contracts by 0.01mm. Calculate the sectional dimensions of the post.
Solution:
Given:
Load (P) = 150 kN
Contraction (δ) = 0.01 mm
Let the dimensions of the post be b and 2b, where b is the smaller dimension.
Formula:
The formula for the contraction or strain (δ) in a rectangular post under load (P) is given as:
δ = (PL)/(AE)
Where L is the length of the post, A is the area of cross-section, E is the Young’s modulus and P is the load acting on the post.
From the problem statement, we can also write:
A = b x 2b = 2b^2
And,
E = 10 GPa = 10 x 10^9 N/m^2
Substituting these values in the strain equation, we get:
0.01 = (150 x 10^3 x L)/(2b^2 x 10 x 10^9)
Simplifying this equation, we get:
L/b^2 = 6.67
Now, we can assume any value for b and calculate the corresponding value of L. For example, if we assume b = 10 mm, then we get:
L = 6.67 x b^2 = 6.67 x 10^2 = 667 mm
Therefore, the dimensions of the post are:
b = 10 mm
2b = 20 mm
And the length of the post is:
L = 667 mm
Conclusion:
Thus, we can calculate the sectional dimensions of a rectangular post under load, given the load and the contraction or strain. It is important to note that the dimensions of the post depend on the assumptions made, and the actual dimensions may vary based on the material properties and the load conditions.
Solution:
Given:
Load (P) = 150 kN
Contraction (δ) = 0.01 mm
Let the dimensions of the post be b and 2b, where b is the smaller dimension.
Formula:
The formula for the contraction or strain (δ) in a rectangular post under load (P) is given as:
δ = (PL)/(AE)
Where L is the length of the post, A is the area of cross-section, E is the Young’s modulus and P is the load acting on the post.
From the problem statement, we can also write:
A = b x 2b = 2b^2
And,
E = 10 GPa = 10 x 10^9 N/m^2
Substituting these values in the strain equation, we get:
0.01 = (150 x 10^3 x L)/(2b^2 x 10 x 10^9)
Simplifying this equation, we get:
L/b^2 = 6.67
Now, we can assume any value for b and calculate the corresponding value of L. For example, if we assume b = 10 mm, then we get:
L = 6.67 x b^2 = 6.67 x 10^2 = 667 mm
Therefore, the dimensions of the post are:
b = 10 mm
2b = 20 mm
And the length of the post is:
L = 667 mm
Conclusion:
Thus, we can calculate the sectional dimensions of a rectangular post under load, given the load and the contraction or strain. It is important to note that the dimensions of the post depend on the assumptions made, and the actual dimensions may vary based on the material properties and the load conditions.
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A short timber post of rectangular section has one side of the section twice the other. when the post loaded with 150kn it contract's by 0.01mm. calculate yhe sectional dimensions of the post?
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A short timber post of rectangular section has one side of the section twice the other. when the post loaded with 150kn it contract's by 0.01mm. calculate yhe sectional dimensions of the post? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A short timber post of rectangular section has one side of the section twice the other. when the post loaded with 150kn it contract's by 0.01mm. calculate yhe sectional dimensions of the post? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A short timber post of rectangular section has one side of the section twice the other. when the post loaded with 150kn it contract's by 0.01mm. calculate yhe sectional dimensions of the post?.
A short timber post of rectangular section has one side of the section twice the other. when the post loaded with 150kn it contract's by 0.01mm. calculate yhe sectional dimensions of the post? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A short timber post of rectangular section has one side of the section twice the other. when the post loaded with 150kn it contract's by 0.01mm. calculate yhe sectional dimensions of the post? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A short timber post of rectangular section has one side of the section twice the other. when the post loaded with 150kn it contract's by 0.01mm. calculate yhe sectional dimensions of the post?.
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