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

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

Please show a hand written solution and the exact fbd for the solution. Thank you!
2. The details of showing that the corresponding dimensionless drag force (Ca) per unit length on the cylinder can be written as Ca = f(Re) Show the explanation
Work on Octive Online.
Engineering Mechanics- II (Dynamics) Ind. Assignment- 1 1. The velocity of a particle is given by v = 25t² - 80t - 200, where v is in feet per second and t is in seconds. Plot the velocity v and acceleration versus time for the first 6 seconds of motion and evaluate the velocity when acceleration is zero.
For a Newtonian fluid flowing in turbulent flow conditions, show the effect of increasing the flow rate by 2 times on the pressure difference and the effect of increasing the pipe diameter by 25% on the pressure difference mathematically (without using numerical values). On the condition that everything else remains constant, show the effect of increasing the pipe diameter on the flow, the effect of increasing the pipe length on the pressure difference and the effect of increasing the pipe length on the flow mathematically (without using numerical values).Show mathematically (without using numerical values) how the pressure difference will be affected if you use two parallel pipelines with a length equal to half the length of the first pipe and equal diameter to the first pipe instead of one long pipeline.
B) Solve the following differential equation:- 3x2 y =0
help pls
Euler Cauch equation is used to solve * Non linear differential equation Linear differential equation O Linear and non linear differential equation O Homogenous differential equation Non of the above
d) The viscosity of a fluid is to be measured using a viscometer constructed of two 750 mm long concentric cylinders. The outer diameter of the inner cylinder is 150 mm and the gap between the two cylinders is 1.2 mm. The inner cylinder is rotated at 200 rpm and the torque is measured to be 10 Nm. a) Derive a generals expression for the viscosity of a fluid using this type of viscometer, and; b) Determine the viscosity of the fluid for the experiment above. Shaft е -Cylinder - Velocity Profile