Calculate by hand the deformation of *joint* 2 of the following simple beam using the *Virtual Work Method*.

**Hint for solution**

According to the method; the integral should be considered separately for the bars between 1-2 and 2-3 nodes.

**Detailed solution**

**E=** Modulus of elasticity **A=** Cross-sectional area **I=** Cross-section moment of inertia

**M=** Moment due to external loading **M'=** Moment due to unit loading **Δ=** Deformation

__Step 1 Finding Moment function by Unit Loading__

**Q:** unit load D_{1} , **D**_{3} : *Support responses* **M'(2):** *2 DN moment value* **L:** Element length

**M'**_{1-2} (x): 1-2 *Moment function* **M**_{2-3} (x): 2- 3 *Moment function* **ΣM**_{1,dn}: Total moment relative to 1 DN.

**ΣD:** Total balance

**Moment Function 1-2 :**

**Moment Function 2-3 :**

__Step 2: Finding the Moment Function Based on the Given Load__

**q: **Distributed load D_{1} , **D**_{3} : Support responses **M(2):** 2 DN moment value **L:** Element length

**M(x):** Moment function** ΣM**_{1,dn} : Total moment with respect to 1 DN.

**ΣD: **Total balance

**Moment Function :**

__Step 3: Multiplying the M and M' Moment Functions in the Previous Steps and Getting the Integral__

__Integral for 1-2 Bar__

__Integral for 2-3 Bar__

**Deformation of node 2 = 0.107m**