Question

A simply supported I-beam is loaded with a distributed load, as shown. The deflection, y, of the center line of the beam as a function of the position, x, is given by the equation: y = (w0x / 360LEI) * (7L^4 - 10L^2x^2 + 3x^4) where L = 4 m is the length, E = 70 GPa is the elastic modulus, I = 52.9 x 10^-6 m^4 is the moment of inertia, and w0 = 20 kN/m. Find the position x where the deflection of the beam is maximum, and determine the deflection at this point. (The maximum deflection is at the point where dy/dx = 0) 1. Determine graphically the highest real root of the polynomial (10 points) 2. The root of the equation using secant method, calculate the error ? for each iteration, use Xa= 1.5 and Xb=2.5, find carry out the first five iterations (30 points) 3. Find the root of the equation using Newton's Raphson method. And calculate the error ? for each iteration, start at x = 3 and carry out the first five iterations. (30 points) 4. Find the root of the equation using False position method, calculate the error ? for each iteration, carry out the first five iterations select the two integers around the solution as initial values (20 points) 5. Analyze results by comparing the different methods used in the previous questions (10 points)

          A simply supported I-beam is loaded with a distributed load, as shown. The deflection, y, of the center line of the beam as a function of the position, x, is given by the equation:
y = (w0x / 360LEI) * (7L^4 - 10L^2x^2 + 3x^4)
where L = 4 m is the length, E = 70 GPa is the elastic modulus, I = 52.9 x 10^-6 m^4 is the moment of inertia, and w0 = 20 kN/m. Find the position x where the deflection of the beam is maximum, and determine the deflection at this point. (The maximum deflection is at the point where dy/dx = 0)
1. Determine graphically the highest real root of the polynomial (10 points)
2. The root of the equation using secant method, calculate the error ? for each iteration, use Xa= 1.5 and Xb=2.5, find carry out the first five iterations (30 points)
3. Find the root of the equation using Newton's Raphson method. And calculate the error ? for each iteration, start at x = 3 and carry out the first five iterations. (30 points)
4. Find the root of the equation using False position method, calculate the error ? for each iteration, carry out the first five iterations select the two integers around the solution as initial values (20 points)
5. Analyze results by comparing the different methods used in the previous questions (10 points)

A simply supported I-beam is loaded with a distributed load, as shown. The deflection, y, of the center line of the beam as a function of the position, x, is given by the equation:
y = (w0x / 360LEI) * (7L^4 - 10L^2x^2 + 3x^4)
where L = 4 m is the length, E = 70 GPa is the elastic modulus, I = 52.9 x 10^-6 m^4 is the moment of inertia, and w0 = 20 kN/m. Find the position x where the deflection of the beam is maximum, and determine the deflection at this point. (The maximum deflection is at the point where dy/dx = 0)
1. Determine graphically the highest real root of the polynomial (10 points)
2. The root of the equation using secant method, calculate the error ? for each iteration, use Xa= 1.5 and Xb=2.5, find carry out the first five iterations (30 points)
3. Find the root of the equation using Newton's Raphson method. And calculate the error ? for each iteration, start at x = 3 and carry out the first five iterations. (30 points)
4. Find the root of the equation using False position method, calculate the error ? for each iteration, carry out the first five iterations select the two integers around the solution as initial values (20 points)
5. Analyze results by comparing the different methods used in the previous questions (10 points)

Added by Dale H.

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