Beam buckling criterion?

If I have an I beam which I subject to some bending load, how can I calculate when the thinner middle part of the I beam will buckle? I though I could use Euler's critical load formula here, but it's unclear to me how exactly I calculate the compression load of the middle part of the beam

Shear buckling of beam web happens when the shear at a section of the beam under consideration surpasses the controlling combination of factored shear.

The following three equations are the LFRD method for:

1. no web instability
2. Inelastic web buckling
3. Elastic web buckling

These depend on the ratio $$h/t$$ of the web. If this ratio is bigger than 260 web stiffeners are required.

Design for shear per AISC (LRFD SPEC F2)

• $$\varphi v$$ resistance factor for shear (0.9)
• $$h$$ web height
• $$t_w$$ web thickness
• $$V_u$$ controlling combination of factored shear
• $$V_n$$ nominal shear strength $$=0.60F_yA_w$$
• $$F_{yw}$$ yield stress of the web (ksi)
• $$A_w$$ web area, the overall depth d times the web thickness wt

Design equation for $$\dfrac{h}{t_w} \leq 260$$ :

The design shear strength of the unstiffened web is $$\varphi V_n$$, where $$V_u \leq \varphi V_n$$.

$$V_n = \begin{cases} 0.6 F_{yw}A_w & \text{if } h/t_w \leq 2.45\sqrt{\dfrac{E}{F_{yw}}}=59\ (\text{for 50ksi steel})\\ 0.6 F_{yw}A_w\left(2.45 \dfrac{\sqrt{E/F_{yw}}}{h/t_w}\right) & \text{if } h/t_w \in \left(2.45 \dfrac{\sqrt{E/F_{yw}}}{h/t_w},\ 3.07 \sqrt{\dfrac{E}{F_{yw}}}\right] \\ A_w \dfrac{4.52E}{(h/t_w)^2} & \text{if } h/t_w \in \left(3.07 \sqrt{\dfrac{E}{F_{yw}}},\ 260\right] \end{cases}$$

What you want to look for is Shear buckling or Web buckling. It is quite an advanced subject though.

In order to determine mode of failure, critical loads etc, you need to specify explicity the boundary conditions, and then solve the problem for the dimensions.

In case that you want to determine the permissible load of the member outside the context of a structure (i.e. Similar calculations as kamran) the similar equations for SI units can be found from the European standards Eurocode 3: BS EN 1993-1-3 Design of steel structures. Section 6.1.7 Covers local transverse forces which is what you are asking.