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Let æ represent the distance from the free end of the beam. Write the moment function in terms of æ using the standard sign convention for beams uhen

Let æ represent the distance from the free end of the beam. Write the moment function in terms of æ using the standard sign convention for beams uhen

Elements Of Electromagnetics
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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SOLVE CAREFULLY!! Please Write Clearly and Box the final Answer for Part A, Part B with THE CORRECT UNITS! Thank you Express your answer to three significant figures and include appropriate units.
Learning Goal: To use integration to find the equation for the elastic curve of a beam. Part A - The moment function For beams with small deflections, the shape of the elastic curve is related to the internal bending d?v moment by the equation EI = M(x), where da? x is the position along the beam as measured from the free end of the beam, v is the transverse Let x represent the distance from the free end of the beam. Write the moment function in terms of x using the standard sign convention for beams. Express your answer so the moment is in kN. m when r is in m. displacement, E is the elastic modulus of the • View Available Hint(s) material, and I is the moment of inertia for the section. The equation for the elastic curve can be determined by integrating this equation twice with respect to x and using boundary conditions to solve for the constants of integration. The standard sign convention for beams is that the internal bending moment is positive when it acts to make the beam vec ? M(x) = concave up. Consider a cantilever beam with span L = 3 m that has a point force P = 15 kN and couple moment Mo = 8 kN - m applied at the free end, as shown. (Figure 1)The beam has E = 200 GPa and I = 5x104 cm Submit Part B - The elastic curve Let x represent the distance from the free end of the beam. Write the equation for the elastic curve for the beam. Express your answer so the deflection is in mm when æ is in m. • View Available Hint(s) Figure 1 of 1> V ΑΣφ ? vec P v(x) = Submit
Transcribed Image Text:Learning Goal: To use integration to find the equation for the elastic curve of a beam. Part A - The moment function For beams with small deflections, the shape of the elastic curve is related to the internal bending d?v moment by the equation EI = M(x), where da? x is the position along the beam as measured from the free end of the beam, v is the transverse Let x represent the distance from the free end of the beam. Write the moment function in terms of x using the standard sign convention for beams. Express your answer so the moment is in kN. m when r is in m. displacement, E is the elastic modulus of the • View Available Hint(s) material, and I is the moment of inertia for the section. The equation for the elastic curve can be determined by integrating this equation twice with respect to x and using boundary conditions to solve for the constants of integration. The standard sign convention for beams is that the internal bending moment is positive when it acts to make the beam vec ? M(x) = concave up. Consider a cantilever beam with span L = 3 m that has a point force P = 15 kN and couple moment Mo = 8 kN - m applied at the free end, as shown. (Figure 1)The beam has E = 200 GPa and I = 5x104 cm Submit Part B - The elastic curve Let x represent the distance from the free end of the beam. Write the equation for the elastic curve for the beam. Express your answer so the deflection is in mm when æ is in m. • View Available Hint(s) Figure 1 of 1> V ΑΣφ ? vec P v(x) = Submit
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