Challenge: Calculate Beam Deflection
Understanding how beams deflect under load is a fundamental part of structural engineering, as it helps ensure that structures remain safe, serviceable, and comfortable for users. Earlier, you explored how to model beams and apply loads in Python. Now, you will build on that knowledge by focusing on the calculation of maximum deflection for a simply supported beam subjected to a uniform distributed load. This calculation is vital in real-world design, as excessive deflection may compromise both the safety and usability of a structure. The standard formula for the maximum deflection of such a beam is:
[ \delta_{max} = \frac{5 w L^4}{384 E I} ]
where w is the load per unit length, L is the length of the beam, E is the modulus of elasticity, and I is the moment of inertia.
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Write a function that computes the maximum deflection of a simply supported beam subjected to a uniform distributed load.
- Use the formula
(5 * w * L ** 4) / (384 * E * I)to calculate the maximum deflection. - The function should accept four parameters:
w,L,E, andI. - Return the calculated maximum deflection.
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Can you explain what each variable in the formula represents?
Can you show an example calculation using this formula?
What are typical values for E and I for common materials?
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Understanding how beams deflect under load is a fundamental part of structural engineering, as it helps ensure that structures remain safe, serviceable, and comfortable for users. Earlier, you explored how to model beams and apply loads in Python. Now, you will build on that knowledge by focusing on the calculation of maximum deflection for a simply supported beam subjected to a uniform distributed load. This calculation is vital in real-world design, as excessive deflection may compromise both the safety and usability of a structure. The standard formula for the maximum deflection of such a beam is:
[ \delta_{max} = \frac{5 w L^4}{384 E I} ]
where w is the load per unit length, L is the length of the beam, E is the modulus of elasticity, and I is the moment of inertia.
Swipe to start coding
Write a function that computes the maximum deflection of a simply supported beam subjected to a uniform distributed load.
- Use the formula
(5 * w * L ** 4) / (384 * E * I)to calculate the maximum deflection. - The function should accept four parameters:
w,L,E, andI. - Return the calculated maximum deflection.
Рішення
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