Calculation of Longitudinal Shear Force VL on Member

The force V_L is the longitudinal shear force between the top surface and the member. It is calculated as an integrated shear flow between the plate and the member at a particular point on the member.

For the simplified example provided here, the resulting cross-section values for the integration width of 10 cm are as follows:

• $${\mathrm{I}}_{\mathrm{y}} = \frac{\mathrm{b} · {\mathrm{h}}^3}{12} = \frac{10 \mathrm{cm} · 20 {\mathrm{cm}}^3}{12} = 6666.67 {\mathrm{cm}}^4$$

  Cross-Section Property I-y
• $${\mathrm{S}}_{\mathrm{y}} = {\mathrm{h}}_1 · \mathrm{b} · \left[\left(\mathrm{h} - {\mathrm{e}}_{\mathrm{z}}\right) - \frac{{\mathrm{h}}_2}{2}\right] = 10 \mathrm{cm} · 10 \mathrm{cm} · \left[\left(20 \mathrm{cm} - 10 \mathrm{cm}\right) - \frac{10 \mathrm{cm}}{2}\right] = 500 {\mathrm{cm}}^3$$

  Cross-Section Property S-y
• $$\mathrm{\tau } = {\mathrm{V}}_{\mathrm{L}} = \frac{{\mathrm{V}}_{\mathrm{z}} · {\mathrm{S}}_{\mathrm{y}}}{{\mathrm{I}}_{\mathrm{y}} · \mathrm{b}} = \frac{5.53 \mathrm{kN} · 500 {\mathrm{cm}}^3}{6666.67 {\mathrm{cm}}^4} = 0.415 \mathrm{kN}/\mathrm{cm} = 41.5 \mathrm{kN}/\mathrm{m}$$

  Cross-Section Property τ

The integration width has been set to the total of 10 cm.

where

The values can be adjusted for a T-beam.

FAQ

FAQ 004340 | When displaying the result diagrams on a member (the "rib" type), there is the option to ...

Cross-Section

Integration Width of Rib