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Write the equations of motion governing the vertical displacements of each of the blocks of weight w = 400 N shown below, measured from the initial undeflected positions of the beams, under the action of gravity alone. You may assume the beams to be massless with Young's modulus E = 200 GPa, second moment of cross-sectional area I = 2 × 105 mm*, and length L = 8 m. You may also assume damping to be negligible. Use the sign convention wherein downward displacements are positive. Ensure you use consistent units and an appropriate number of significant digits to represent all quantities. For each case, state the units in which the acceleration and displacement of the block will be computed upon solving the equation of motion. Hint: You are only asked to write the differential equations governing the motion of the blocks; you are not required to solve any of these differential equations. You may use stan- dard beam deflection equations in your solutions, without deriving them. (1) EI L/2 L/2

Write the equations of motion governing the vertical displacements of each of the blocks of weight w = 400 N shown below, measured from the initial undeflected positions of the beams, under the action of gravity alone. You may assume the beams to be massless with Young's modulus E = 200 GPa, second moment of cross-sectional area I = 2 × 105 mm*, and length L = 8 m. You may also assume damping to be negligible. Use the sign convention wherein downward displacements are positive. Ensure you use consistent units and an appropriate number of significant digits to represent all quantities. For each case, state the units in which the acceleration and displacement of the block will be computed upon solving the equation of motion. Hint: You are only asked to write the differential equations governing the motion of the blocks; you are not required to solve any of these differential equations. You may use stan- dard beam deflection equations in your solutions, without deriving them. (1) EI L/2 L/2

Materials Science And Engineering Properties
Materials Science And Engineering Properties
1st Edition
ISBN:9781111988609
Author:Charles Gilmore
Publisher:Charles Gilmore
Chapter8: Engineering Materials
Section: Chapter Questions
Problem 85CQ
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Write the equations of motion governing the vertical displacements of each of the blocks of weight w= 400 N shown below, measured from the initial undeflected positions of the beams, under the action of gravity alone. You may assume the beams to be massless with Young's modulus E = 200 GPa, second moment of cross-sectional area I = 2x 105 mm*, and length L = 8 m. You may also assume damping to be negligible. Use the sign convention wherein downward displacements are positive. Ensure you use consistent units and an appropriate number of significant digits to represent all quantities. For each case, state the units in which the acceleration and displacement of the block will be computed upon solving the equation of motion. Hint: You are only asked to write the differential equations governing the motion of the blocks; you are not required to solve any of these differential equations. You may use stan- dard beam deflection equations in your solutions, without deriving them. (i) EI L/2 L/2
Transcribed Image Text:Write the equations of motion governing the vertical displacements of each of the blocks of weight w= 400 N shown below, measured from the initial undeflected positions of the beams, under the action of gravity alone. You may assume the beams to be massless with Young's modulus E = 200 GPa, second moment of cross-sectional area I = 2x 105 mm*, and length L = 8 m. You may also assume damping to be negligible. Use the sign convention wherein downward displacements are positive. Ensure you use consistent units and an appropriate number of significant digits to represent all quantities. For each case, state the units in which the acceleration and displacement of the block will be computed upon solving the equation of motion. Hint: You are only asked to write the differential equations governing the motion of the blocks; you are not required to solve any of these differential equations. You may use stan- dard beam deflection equations in your solutions, without deriving them. (i) EI L/2 L/2
(ii) EI (ii) EI L/2 L/2
Transcribed Image Text:(ii) EI (ii) EI L/2 L/2
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