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Examples of Governing Differential Equations, Boundary Conditions, Initial Conditions, and Exact Solutions for Some Engineering Problems ТАBLE 18.8 Governing Equation, Boundary Conditions or Initial Conditions Problem Type Solution Example 1: The deflection of a beam. wX(L – X) Deflection of the bearn Y, as the El- function of distance X: 2 Boundary conditions: at X = 0, Y - 0 and at X = L, Y – 0 X4 + 2LX – EX) 24EI E,I Example 3: The temperature distribu- tion along a long fin. hp dX? kA Temperature distribution along the fin as the function of X: (T-T) = 0 Example 2: The oscillation of an elastic d' y +wy – o dt? The position of the mass y, as the function of time: y(t)= y, cos le,? system. k where w? = undary conditions: at X - 0,T-e T = T„+(Tose-Tu )e Tair, h Tpase as L- o,T = T. Initial conditions: at time t = 0, Yo y = y, and at time t = 0,0y = 0 dt P = Perimeter

Examples of Governing Differential Equations, Boundary Conditions, Initial Conditions, and Exact Solutions for Some Engineering Problems ТАBLE 18.8 Governing Equation, Boundary Conditions or Initial Conditions Problem Type Solution Example 1: The deflection of a beam. wX(L – X) Deflection of the bearn Y, as the El- function of distance X: 2 Boundary conditions: at X = 0, Y - 0 and at X = L, Y – 0 X4 + 2LX – EX) 24EI E,I Example 3: The temperature distribu- tion along a long fin. hp dX? kA Temperature distribution along the fin as the function of X: (T-T) = 0 Example 2: The oscillation of an elastic d' y +wy – o dt? The position of the mass y, as the function of time: y(t)= y, cos le,? system. k where w? = undary conditions: at X - 0,T-e T = T„+(Tose-Tu )e Tair, h Tpase as L- o,T = T. Initial conditions: at time t = 0, Yo y = y, and at time t = 0,0y = 0 dt P = Perimeter

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Table 18.8 , verify that the given solution satisfies the governing differential equation and the boundary conditions.

Examples of Governing Differential Equations, Boundary Conditions, Initial Conditions, and Exact Solutions for Some Engineering Problems ТАBLE 18.8 Governing Equation, Boundary Conditions or Initial Conditions Problem Type Solution Example 1: The deflection of a beam. wX(L – X) Deflection of the bearn Y, as the El- function of distance X: 2 Boundary conditions: at X = 0, Y - 0 and at X = L, Y – 0 X4 + 2LX – EX) 24EI E,I Example 3: The temperature distribu- tion along a long fin. hp dX? kA Temperature distribution along the fin as the function of X: (T-T) = 0 Example 2: The oscillation of an elastic d' y +wy – o dt? The position of the mass y, as the function of time: y(t)= y, cos le,? system. k where w? = undary conditions: at X - 0,T-e T = T„+(Tose-Tu )e Tair, h Tpase as L- o,T = T. Initial conditions: at time t = 0, Yo y = y, and at time t = 0,0y = 0 dt P = Perimeter
Transcribed Image Text:Examples of Governing Differential Equations, Boundary Conditions, Initial Conditions, and Exact Solutions for Some Engineering Problems ТАBLE 18.8 Governing Equation, Boundary Conditions or Initial Conditions Problem Type Solution Example 1: The deflection of a beam. wX(L – X) Deflection of the bearn Y, as the El- function of distance X: 2 Boundary conditions: at X = 0, Y - 0 and at X = L, Y – 0 X4 + 2LX – EX) 24EI E,I Example 3: The temperature distribu- tion along a long fin. hp dX? kA Temperature distribution along the fin as the function of X: (T-T) = 0 Example 2: The oscillation of an elastic d' y +wy – o dt? The position of the mass y, as the function of time: y(t)= y, cos le,? system. k where w? = undary conditions: at X - 0,T-e T = T„+(Tose-Tu )e Tair, h Tpase as L- o,T = T. Initial conditions: at time t = 0, Yo y = y, and at time t = 0,0y = 0 dt P = Perimeter
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