Homework Answers
Q40
False statement is : For a prismatic beam: M is constant.
The differential equation of flexure of beam is valid for beam having same equation of bending moment through out the beam. It is not necessary that the beam is of constant bending moment.
Q41
Correct statement is : Boundary conditions are always needed to determine the elastic curve. It is a second order differential equation so we need two boundary conditions to solve the problem.
Q42
First option is correct because, at the cantilever side slope is zero and at the moment applied point the slope is non-zero.
Q43
Second option is correct.
Curvature is d^2y/dx^2 and R is radius of curvature. From the differential equation of flexure of beam it is clear that local curvature is proportional to the bending moment.
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help on these 4 multiple choice questions
Question 40 2 About the differential equation that describes...
help Question 36 2ts Based on the following appendix from the text book of Mechanics of...
help
Question 36 2ts Based on the following appendix from the text book of Mechanics of Materials byBeered Appendix Beam Deflections and Steps 13 - ER which of the following statements is true about the boundary conditions for situation 13-cartier beam with clockwise bending moment at the rightend 2=LO - -0-0 = 0, y = 0 EL-M O-0-0 Question 37 2 pts About the differential equation that describes the elastic curve for a bear which of the following statements is...
2. The governing differential equation that relates the deflection y of a beam to the load w ia w...
2. The governing differential equation that relates the deflection y of a beam to the load w ia where both y and w are are functions of r. In the above equation, E is the modulus of elasticity and I is the moment of inertia of the beam. For the beam and loading shown in the figure, first de m, E = 200 GPa, 1 = 100 × 106 mm4 and uo 100 kN/m and determine the maximum deflection. Note...
Question. 4 (20%) A uniformly loaded beam of length "L" is supported at both ends. The deflection y(x) is a function of horizontal position x and is given by the differential equation on...
Question. 4 (20%) A uniformly loaded beam of length "L" is supported at both ends. The deflection y(x) is a function of horizontal position x and is given by the differential equation on dEl d1 Beat dE 4() Assume q(x) is constant. Determine the equation for y(x) in terms of different variables. Hint: Use laplace transform. Below are boundary conditions: (L)ono dene y"(o) o no deflection at x= 0 and L no bending moment at x 0 and L y...
This is a question about Partial differential equation - Heat equation. Please help solving part (a)...
This is a question about
Partial differential equation - Heat equation. Please help solving
part (a) and show clear explanations. Thanks!
=K х 7. The temperature T(2,t) in an insulated rod of length L and diffusivity k is given by the heat equation ОТ 22T 0 < x < L. at Əx2' Initially this rod is at constant temperature To, and immediately after t=0 the temperature at x = L is suddenly increased to T1. The temperature at x =...
Hello, I need your help for this question which is highly related with differancial equation in a...
Hello, I need your help for this question which is
highly related with differancial equation in advanced math and a
bit related with civil engineering.
My best regards...
1. The differential equation of the elastic curve of an eccentrically loaded column is Here is deflection, E the modulus of elasticity of the column 1 the moment of inertia of the cross-section of the column, P the axial load, and e is the eccentricity. Draw the deflection of the steel column...
3. The last question is about physical interpretation of PDES. Assume throughout that u(r, t) describes...
3. The last question is about physical interpretation of PDES. Assume throughout that u(r, t) describes the temperature in a thin rod, with r [0, L] andt2 0. Note: when I ask for physical interpretation, I mean things like "u(0,t) = 0 means that fixing one of the ends at constant temperature" (a) Consider the IBVP we are O (3 points) at Or2 u(0, t) Ou (L, t) u(x,0) =0 Give a physical interpretation of the boundary conditions and of...
help with all except numbers 21-26 16. Solve the differential equation by using the Cauchy-Euler Equation 17. Find the solution to the given Initial Value Problem using Green's Theorem 0,y'...
help with all except numbers 21-26
16. Solve the differential equation by using the Cauchy-Euler Equation 17. Find the solution to the given Initial Value Problem using Green's Theorem 0,y'(0)s 0 y(0) y" + 6y' + 9y x, 18. Find the solution to the given Boundary Value Problem y" ty-1, y(O)0, y(1) 19. Solve the system of differential equations by systematic elimination. dy dt dt 20. Use any procedure in Chapter 4 to solve the differential equation subjected to the...
Elementary Differential Equation Unit Step Function Problem Project 2 A Spring-Mass Event Problenm A mass of...
Elementary Differential Equation Unit Step Function Problem
Project 2 A Spring-Mass Event Problenm A mass of magnitude m is confined to one-dimensional motion between two springs on a frictionless horizontal surface, as shown in Figure 4.P.3. The mass, which is unattached to either spring, undergoes simple inertial motion whenever the distance from the origin of the center point of the mass, x, satisfies lxl < L. When x 2 L, the mass is in contact with the spring on the...
Question 1. Substitution of given form of solution and hyperbolic functions. The non-linear ordinary differential equat...
Question 1. Substitution of given form of solution and hyperbolic functions. The non-linear ordinary differential equation describing the smooth shape of a structural arch of constant thickness in mechanical equilibrium under its own weight per unit length w, and a horizontal compressive force T, is (y")2 = k2(1 + (y')"). Here k is a known constant and y(x) is the vertical height of the arch at position x, the horizontal distance from a given reference point. (a) Using hyperbolic function...
Question 24 1 pts Using the shooting method for the following second-order differential equation governing the...
Question 24 1 pts Using the shooting method for the following second-order differential equation governing the boundary value problem G.E: + EA (x) +u = L (x) € (0,L] B.C's: u () = 0 and EA (2) de Iz-L=F, the trapezoidal method is used to converts the problem into coupled integral equations solved at the quadrature points. None of the above. finite differences are used to convert the governing equation and boundary conditions of the problem into an analog set...
help
Question 36 2ts Based on the following appendix from the text book of Mechanics of Materials byBeered Appendix Beam Deflections and Steps 13 - ER which of the following statements is true about the boundary conditions for situation 13-cartier beam with clockwise bending moment at the rightend 2=LO - -0-0 = 0, y = 0 EL-M O-0-0 Question 37 2 pts About the differential equation that describes the elastic curve for a bear which of the following statements is...
2. The governing differential equation that relates the deflection y of a beam to the load w ia where both y and w are are functions of r. In the above equation, E is the modulus of elasticity and I is the moment of inertia of the beam. For the beam and loading shown in the figure, first de m, E = 200 GPa, 1 = 100 × 106 mm4 and uo 100 kN/m and determine the maximum deflection. Note...
Question. 4 (20%) A uniformly loaded beam of length "L" is supported at both ends. The deflection y(x) is a function of horizontal position x and is given by the differential equation on dEl d1 Beat dE 4() Assume q(x) is constant. Determine the equation for y(x) in terms of different variables. Hint: Use laplace transform. Below are boundary conditions: (L)ono dene y"(o) o no deflection at x= 0 and L no bending moment at x 0 and L y...
This is a question about
Partial differential equation - Heat equation. Please help solving
part (a) and show clear explanations. Thanks!
=K х 7. The temperature T(2,t) in an insulated rod of length L and diffusivity k is given by the heat equation ОТ 22T 0 < x < L. at Əx2' Initially this rod is at constant temperature To, and immediately after t=0 the temperature at x = L is suddenly increased to T1. The temperature at x =...
Hello, I need your help for this question which is
highly related with differancial equation in advanced math and a
bit related with civil engineering.
My best regards...
1. The differential equation of the elastic curve of an eccentrically loaded column is Here is deflection, E the modulus of elasticity of the column 1 the moment of inertia of the cross-section of the column, P the axial load, and e is the eccentricity. Draw the deflection of the steel column...
3. The last question is about physical interpretation of PDES. Assume throughout that u(r, t) describes the temperature in a thin rod, with r [0, L] andt2 0. Note: when I ask for physical interpretation, I mean things like "u(0,t) = 0 means that fixing one of the ends at constant temperature" (a) Consider the IBVP we are O (3 points) at Or2 u(0, t) Ou (L, t) u(x,0) =0 Give a physical interpretation of the boundary conditions and of...
help with all except numbers 21-26
16. Solve the differential equation by using the Cauchy-Euler Equation 17. Find the solution to the given Initial Value Problem using Green's Theorem 0,y'(0)s 0 y(0) y" + 6y' + 9y x, 18. Find the solution to the given Boundary Value Problem y" ty-1, y(O)0, y(1) 19. Solve the system of differential equations by systematic elimination. dy dt dt 20. Use any procedure in Chapter 4 to solve the differential equation subjected to the...
Elementary Differential Equation Unit Step Function Problem
Project 2 A Spring-Mass Event Problenm A mass of magnitude m is confined to one-dimensional motion between two springs on a frictionless horizontal surface, as shown in Figure 4.P.3. The mass, which is unattached to either spring, undergoes simple inertial motion whenever the distance from the origin of the center point of the mass, x, satisfies lxl < L. When x 2 L, the mass is in contact with the spring on the...
Question 1. Substitution of given form of solution and hyperbolic functions. The non-linear ordinary differential equation describing the smooth shape of a structural arch of constant thickness in mechanical equilibrium under its own weight per unit length w, and a horizontal compressive force T, is (y")2 = k2(1 + (y')"). Here k is a known constant and y(x) is the vertical height of the arch at position x, the horizontal distance from a given reference point. (a) Using hyperbolic function...
Question 24 1 pts Using the shooting method for the following second-order differential equation governing the boundary value problem G.E: + EA (x) +u = L (x) € (0,L] B.C's: u () = 0 and EA (2) de Iz-L=F, the trapezoidal method is used to converts the problem into coupled integral equations solved at the quadrature points. None of the above. finite differences are used to convert the governing equation and boundary conditions of the problem into an analog set...
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