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# Mohr's Method - displacement calculation

**In this text you will learn**about what

**Mohr's Method**is and what is the algorithm for solving problems involving

**displacements**using this method.

### Mohr's Method

**Mohr's Method**, also known as

**grapho-analytical method, equivalent beam method, secondary loading method, or graphical method**, is based on a two-step approach for solving the problem of determining the distribution of bending moments in a beam.

In the first step, we deal with the standard distribution of shear forces in a specific (given) beam. Then, in the second step, we focus on determining the distribution of moments in the so-called "equivalent beam".

For the

**equivalent beam (secondary, fictitious beam)**, we choose the geometry, support, and loading in such a way that, based on the solution of the first step, we obtain a distribution of moments that is numerically identical to the deflection distribution in the real beam.

To better understand, please see the example below

### Algorithm

Procedure for solving a problem
**• determine the bending moment diagram in the real beam (assuming positive moments on the bottom of the beam),
• determine the equivalent/fictitious beam (according to the table below),
• load the equivalent/fictitious beam with the bending moment diagram from the real beam divided by its bending stiffness EI.**

**• determine the shear force and/or bending moment at the selected point in the equivalent beam, labeled as:**

They will be equal to the corresponding displacements at the same point in the axis of the real beam.

-> The shear force at point K in the equivalent beam corresponds to the rotation angle at point K in the real beam,

\(\varphi(x)=Q_f (x) \)

-> The bending moment at point K in the equivalent beam corresponds to the deflection of the real beam at that point.

\( w(x)=M_f (x)\)

In the adopted reference system, displacement w>0 is directed downward, and a positive rotation angle \(\varphi>0\) is consistent with clockwise rotation.

#### Example - Mohr's Method - transformation of supports from primary beam to secondary

#### Solution

#### Example - Mohr's Method - effect of temperature

#### Solution

Of course, Mohr's Method can also be used to calculate deflections caused by temperature. We use the formula:\(\kappa=\frac{\alpha \Delta T}{h}\)

Then, the load on the fictitious beam has the value of κ and is directed towards the warmer fibers.