D12.A.6.2 Single symmetric wide flange profile and tapered section
The von Mises stress is checked at nine stress points as shown in figure below.
Stress points checked for a singly symmetric wide flange section
Section properties
- A_{x}, I_{x} , I_{y}, and I_{z} are taken from STAAD.Pro database, except for tapered sections where these values are calculated for each section checked. (i.e., Iz, Iy values are taken from the middle of the member.)
- ${A}_{z}=2/3(b\cdot t+{b}_{1}\cdot {t}_{1})$
- ${C}_{w}=\frac{{b}^{3}t\cdot {b}_{1}^{3}{t}_{1}{(h-t/2-{t}_{1}/2)}^{2}}{12({b}^{3}t+{b}_{1}^{3}{t}_{1})}$ref. NS app. C3
Refer to D12.A.6.1 Double symmetric wide flange profile for equations used in section property calculations.
Stress calculation
Refer to D12.A.6.1 Double symmetric wide flange profile for equations used in general stress calculations.
Where the component stresses are calculated as shown in the following table:
Point No | σ_{x} | σ_{by} | σ_{bz} | τ_{x} | τ_{y} | τ_{z} |
---|---|---|---|---|---|---|
1 | $\frac{{F}_{x}}{{A}_{x}}$ | $-\frac{{M}_{y}}{{I}_{y}}\frac{b}{2}$ | $\frac{{M}_{z}}{{I}_{z}}{h}_{2}$ | $\frac{{M}_{x}}{{I}_{x}}t$ | 0 | 0 |
2 | " | 0 | " | " | $\frac{{F}_{y}}{{I}_{z}}\frac{bt({h}_{1}+t/2)}{2t}$ | $\frac{{F}_{z}}{{I}_{y}}\frac{t{b}^{2}}{8t}$ |
3 | " | $\frac{{M}_{y}}{{I}_{y}}\frac{b}{2}$ | " | " | 0 | 0 |
4 | " | 0 | $\frac{{M}_{z}}{{I}_{z}}{h}_{1}$ | $\frac{{M}_{x}}{{I}_{x}}s$ | $\frac{{F}_{y}}{{I}_{z}}\frac{bt({h}_{1}+t/2)}{s}$ | 0 |
5 | " | 0 | 0 | " | $\frac{{F}_{y}}{{I}_{z}}\frac{bt({h}_{1}+t/2)+0.5{h}_{1}^{2}s}{s}$ | 0 |
6 | " | 0 | $-\frac{{M}_{z}}{{I}_{z}}{h}_{3}$ | " | $\frac{{F}_{y}}{{I}_{z}}\frac{{b}_{1}{t}_{1}({h}_{3}+{t}_{1}/2)}{s}$ | 0 |
7 | " | $-\frac{{M}_{y}}{{I}_{y}}\frac{{b}_{1}}{2}$ | $-\frac{{M}_{z}}{{I}_{z}}{h}_{4}$ | $\frac{{M}_{x}}{{I}_{x}}t$ | 0 | 0 |
8 | " | 0 | " | " | $\frac{{F}_{y}}{{I}_{z}}\frac{{b}_{1}{t}_{1}({h}_{3}+{t}_{1}/2)}{2{t}_{1}}$ | $\frac{{F}_{z}}{{I}_{y}}\frac{{t}_{1}{b}^{2}}{8{t}_{1}}$ |
9 | " | $\frac{{M}_{y}}{{I}_{y}}\frac{{b}_{1}}{2}$ | " | " | 0 | 0 |
In general wide flange profiles are not suitable for large torsional moments. The reported torsional stresses are indicative only. For members with major torsional stresses a separate evaluation has to be carried out. Actual torsional stress distribution is largely dependent on surface curvature at stress point and warping resistance.