What is plate girder? Preliminary design

A plate girder is a built-up beam of steel plates (a web plate and two flange plates, joined by welds or bolts) used for spans or loads beyond the range of rolled sections, usually for spans above about 15 m, such as in bridges and industrial buildings. The web is deep and thin and is stiffened against buckling.

Preliminary design (sizing) steps

1. Design forces. Find the factored maximum moment $M$ at mid-span and the maximum shear $V$ at the supports (from the loads, including an assumed self-weight).
2. Depth of girder. For economy $d \approx \dfrac{L}{10}$ to $\dfrac{L}{12}$; or, for minimum weight, $d = \left(\dfrac{M\,k}{f}\right)^{1/3}$, with $f = f_y/\gamma_{m0}$ and $k = d/t_w$ (about 100 to 200).
3. Web thickness. $t_w = d/k$. Check the serviceability limits, $d/t_w \le 200\varepsilon$ (unstiffened or widely stiffened) up to about $270\varepsilon$ (closely stiffened), and the flange-buckling limit $d/t_w \le 345\varepsilon_f^2$ (IS 800:2007 cl. 8.6.1). Minimum thickness 8 mm (6 mm sheltered).
4. Flange area. $A_f = \dfrac{M\gamma_{m0}}{f_y\,d} - \dfrac{A_w}{6}$ (web contribution included approximately), where $A_w = d\,t_w$.
5. Flange size. Width $b_f \approx d/3$ to $d/5$ (also $\ge L/40$ for lateral stability); thickness $t_f = A_f/b_f$, with the outstand $b/t_f \le 13.6\varepsilon$ (semi-compact, welded). Round to available plate sizes.
6. Trial check. Find $I_{zz} = \dfrac{t_wd^3}{12} + 2\,b_ft_f\left(\dfrac{d+t_f}{2}\right)^2$ and check the moment capacity $M_d = \beta_bZ_pf_y/\gamma_{m0}$, which for a semi-compact section ($\beta_b = Z_e/Z_p$) becomes $M_d = Z_ef_y/\gamma_{m0}$; the shear capacity $V_d = d\,t_wf_y/(\sqrt3\gamma_{m0})$, or the shear buckling resistance of cl. 8.4.2 when $d/t_w > 67\varepsilon$; and the deflection.
7. After preliminary sizing, the detailed design proceeds with the stiffeners (bearing and intermediate), the flange-to-web welds ($q = VA\bar y/I$), curtailment of the flange plates, and splices.

Remark

The thinner the web, the lighter the girder, but the more stiffeners it needs; the usual choice balances the web weight against the cost of stiffeners and fabrication. The flanges carry the bending as a couple $F = M/d$, and the web carries the shear.