In this guide, we will solve the statically indeterminate system using the force method. It is somewhat complementary to the force method guide – an algorithm, because in that guide there was only theory. Here we will solve a sample task that you can get during a test or exam.

**Exercise.**

Determine the distribution of internal forces M, T, N in a statically indeterminate system using the force method.

**Real system**

**Calculation of the degree of static indeterminate**

**Construction of the basic layout**We reject both ties at point D.

**Arranging a system of canonical equations****Determination of displacements from the Maxwell-Mohr patterns**(we omit the influence of T and N, because their impact on the displacement is insignificant).

5.1.** Graphs of internal forces from hyperstatic load .**

State X1

5.2. **Graphs of internal forces from hyperstatic load .**

State X2

5.3.** Graphs of internal forces from external impact P.**

Stan

5.4** Calculation of displacements δij:** (I will not multiply graphs here by myself, because we can already do it, but if you do not know what’s going on, I invite you to read:** calculating displacements**).

(we multiply the X1 status graphs)

(multiplication of state X1 by X2)

(we multiply the X2 status graphs)

5.5 **Calculation of δip displacement.**

(multiplication of state X1 by state P)

(multiplication of state X2 by state P)

**The solution of the system of canonical equations.**

**Determining the diagram of internal forces in the real system from superposition patterns.**

**7.1. Bending moment **

**7.2. Shear forces**

**7.3. Normal forces**

**Determination of supporting reactions from external force diagrams.**

Checking the equilibrium conditions.

**Static check of correctness of the solution in nodes (node B).**

**All forces are balanced. Static check is correct!**

**Kinematic check**It is necessary to determine the displacement of the cross-section in the real system at the point whose value we know, for example: from the support ties. We know that there must be a zero displacement on the support, when such displacement comes out, it means that we have calculated the task correctly.