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4. The deflection w of a beam of length L, clamped at both ends, and subjected to a uniform distributed load q is given by q Lx3 L²x² x4 w(x)= + + and (Equation 4.1) 2 ΕΙ 12 24 24 where El is the flexural rigidity of the beam. (a) Find the maximum deflection W₁ using Equation 4.1 and express w(x) in terms of Wo. (4 Marks) (b) For the clamped beam in the elastic state, compute the kinetic energy and show that the mass factor of an equivalent single-degree-of-freedom (SDOF) system is 0.41. (c) (5 Marks) Compute the strain energy of the clamped beam in the elastic state and show that the stiffness factor of an equivalent SDOF system is 0.53. (5 Marks) (d) For the clamped beam in the plastic state whereby plastic hinges are formed at both ends and at the mid-span, calculate the mass factor and load factor of an equivalent SDOF system. (6 Marks) (e) Compute the dynamic reactions V(t) of the clamped beam in the plastic state in terms of the maximum resistance Rm and applied force F = qL.

4. The deflection w of a beam of length L, clamped at both ends, and subjected to a uniform distributed load q is given by q Lx3 L²x² x4 w(x)= + + and (Equation 4.1) 2 ΕΙ 12 24 24 where El is the flexural rigidity of the beam. (a) Find the maximum deflection W₁ using Equation 4.1 and express w(x) in terms of Wo. (4 Marks) (b) For the clamped beam in the elastic state, compute the kinetic energy and show that the mass factor of an equivalent single-degree-of-freedom (SDOF) system is 0.41. (c) (5 Marks) Compute the strain energy of the clamped beam in the elastic state and show that the stiffness factor of an equivalent SDOF system is 0.53. (5 Marks) (d) For the clamped beam in the plastic state whereby plastic hinges are formed at both ends and at the mid-span, calculate the mass factor and load factor of an equivalent SDOF system. (6 Marks) (e) Compute the dynamic reactions V(t) of the clamped beam in the plastic state in terms of the maximum resistance Rm and applied force F = qL.

Principles of Foundation Engineering (MindTap Course List)
Principles of Foundation Engineering (MindTap Course List)
8th Edition
ISBN:9781305081550
Author:Braja M. Das
Publisher:Braja M. Das
Chapter6: Vertical Stress Increase In Soil
Section: Chapter Questions
Problem 6.4P: Refer to Figure P6.4. A strip load of q = 900 lb/ft2 is applied over a width B = 36 ft. Determine...
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4. The deflection w of a beam of length L, clamped at both ends, and subjected to a uniform distributed load q is given by q Lx3 L²x² x4 w(x)= + + and (Equation 4.1) 2 ΕΙ 12 24 24 where El is the flexural rigidity of the beam. (a) Find the maximum deflection W₁ using Equation 4.1 and express w(x) in terms of Wo. (4 Marks) (b) For the clamped beam in the elastic state, compute the kinetic energy and show that the mass factor of an equivalent single-degree-of-freedom (SDOF) system is 0.41. (c) (5 Marks) Compute the strain energy of the clamped beam in the elastic state and show that the stiffness factor of an equivalent SDOF system is 0.53. (5 Marks) (d) For the clamped beam in the plastic state whereby plastic hinges are formed at both ends and at the mid-span, calculate the mass factor and load factor of an equivalent SDOF system. (6 Marks) (e) Compute the dynamic reactions V(t) of the clamped beam in the plastic state in terms of the maximum resistance Rm and applied force F = qL.
Transcribed Image Text:4. The deflection w of a beam of length L, clamped at both ends, and subjected to a uniform distributed load q is given by q Lx3 L²x² x4 w(x)= + + and (Equation 4.1) 2 ΕΙ 12 24 24 where El is the flexural rigidity of the beam. (a) Find the maximum deflection W₁ using Equation 4.1 and express w(x) in terms of Wo. (4 Marks) (b) For the clamped beam in the elastic state, compute the kinetic energy and show that the mass factor of an equivalent single-degree-of-freedom (SDOF) system is 0.41. (c) (5 Marks) Compute the strain energy of the clamped beam in the elastic state and show that the stiffness factor of an equivalent SDOF system is 0.53. (5 Marks) (d) For the clamped beam in the plastic state whereby plastic hinges are formed at both ends and at the mid-span, calculate the mass factor and load factor of an equivalent SDOF system. (6 Marks) (e) Compute the dynamic reactions V(t) of the clamped beam in the plastic state in terms of the maximum resistance Rm and applied force F = qL.
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