# Shift of joint in kinematically indeterminate system

Given ist the following system:

$$EI=100000\frac{\text{kN}}{\text{m}^2}$$ $$EA\to \infty$$

I'm suppossed to find the horizontal and vertical shift of joint g. My first approach was to use the principle of virtual work using $$f_i=\int_0^l\frac{M\bar{M}}{EI}dx$$. (As per syllabus, shear forces can be neglected.) In order to determine the moments I need to figure out the reaction forces. However, the system is kinematically indeterminate, despite being statically deteminate.

This can easily be seen by determining the moments around the respective bearings in each system: $$1: G_x+G_y+24=0$$ $$2: G_x + G_y + 48=0$$

Alternatively, it can be seen that there are no conflicting moment poles.

My next approach was the principle of virtual shifts, which (unfortunately as expected) led to the same equations as above.

What is the correct way to approach this problem? Any help would be appreciated!

In case someone wants to know the solution:

$$\delta_x = 29.97\cdot10^{-3}\text{m}$$ $$\delta_y = 7.29\cdot10^{-3}\text{m}$$ $$\delta_{\text{ges}}=30.84\cdot 10^{-3}\text{m}$$