Question

Properly write the stiffness matrix and force equilibrium equation for the following problems. Solve (by hand or using MATLAB} the force equilibrium equation for the unknown forces and/or displacements. X1, F1 x2, F2 1. For the above spring system, F1 = O and F2 = 19 lbf. Spring 1 has a stiffness of k1 = 12 lbflin and Spring 2 has a stiffness of k2 = 13 Ibf/in. Solve for the displacements x1 and x2. 2. Using your results from problem 1, use matrix equations to solve for the support reaction at the wall.

Answer 1

To solve for the displacements x1 and x2, we need to set up the force equilibrium equation and the stiffness matrix.

First, let's define the unknown displacements as x1 and x2. We know that F1 is 0 lbf and F2 is 19 lbf. The stiffness of spring 1 (k1) is 12 lb/in, and the stiffness of spring 2 (k2) is 13 lb/in.

The force equilibrium equation can be written as:

0 = k1 * x1 + k2 * (x2 - x1) - F2

Now, let's set up the stiffness matrix:

| k1 + k2 -k2 |

| -k2 k2 |

To solve for x1 and x2, we can set up the matrix equation:

| k1 + k2 -k2 | | x1 | | F2 |

| -k2 k2 | * | x2 | = | 0 |

We can solve this system of equations either by hand or using MATLAB. By solving this system, we will obtain the values of x1 and x2.

2. To find the support reaction at the wall, we can use the results obtained from problem 1.

Since the wall supports spring 1, the reaction force at the wall can be calculated by using Hooke's Law, which states that the force in a spring is equal to its stiffness multiplied by its displacement.

The support reaction force at the wall is given by:

Reaction Force = k1 * x1

Using the values of k1 and x1 obtained from problem 1, we can calculate the support reaction force at the wall.