When displaying the result diagrams on a member (the "rib" type), there is the option to display the internal force VL. What is this value and how is it calculated?

Answer

The force VL 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:

  • $I_y=\frac{b\times h^3}{12}=\frac{10 cm\times20 cm^3}{12}=6,666.67 cm^4$
  • $S_y=h_1\times b\times((h-e_z)-\frac{h_2}2)=10 cm\times10 cm\times((20 cm-10 cm)-\frac{10 cm}2)=500 cm^3$
  • $\tau=V_L=\frac{V_z\times S_y}{I_y\times b}=\frac{5.53 kN\times500 cm^3}{6,666.67 cm^4}=0.415 kN/cm=41.5 kN/m$
The integration width has been set to the total of 10 cm.

Values:
  • Iy second moment of area
  • Sy statical moment
  • h1 height of the upper cross-section part
  • h2 height of the lower cross-section part
  • ez centroidal distance
  • h total height
The values can be adjusted for a T-beam.

Keywords

T-beam Rib internal forces Shear flow Longitudinal force

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