## Question

# (x) Consider the one-dimensional (1D) discrete system with linear springs depicted in Figure 1 for which we have the following data: 1) Boundary conditions

(x) Consider the one-dimensional (1D) discrete system with linear springs depicted in Figure 1 for which we have the following data: 1) Boundary conditions (fixed support): U1 = 0, 42 = 0 2) External loads: F = 56N 3) Spring constants: K (1) = 3k, k(2) = k, k (3) = 2k, k(4) = k Wanted: Analyze the system in the individual springs and create the equilibrium equations. Calculate the element stiffness matrices and assemble the global stiffness matrix and the global nodal force vector. b) Solve the system for the unknown nodal displacements. Calculate the reaction forces at the supports. 4 =0 (1) 3 -Xm (3) 01-12) = 1 x = 2k (4) 4 k F=56 N www +43 2 4 43 3 Figure 1: One-dimensional (1D) discrete system with linear springs

## Step by Step Solution

There are 3 Steps involved in it

### Step: 1

Solutions Step 1 1 Analyze individual springs and create equilibrium equations Spring 1 Equilibrium equation F 3ku2 u1 Spring 2 Equilibrium equation 0 ku3 u2 Spring 3 Equilibrium equation 56 N 2ku4 u3 ...### Get Instant Access to Expert-Tailored Solutions

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### Step: 2

### Step: 3

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