IQ-CAL-007REV 0NOT A CERTIFICATE
IQEG CALCULATION LAB
Beam shear, moment and deflection
IQ-CAL-007 · Rev 0 Indicative · 11/11/2026 · Not a certificate
INPUTS + RESULTSUNITS AS TABULATED
IQ Engineering Group · Sydney · IQ-CAL-007 · Beam shear, moment and deflection · millimetres, kN, kNm, MPa unless noted
Layout
Glossary
- δ
- Vertical deflection of the elastic curve. Positive up. Downward deflection is negative so the plot is the actual beam shape.
- Query x
- Station on the elevation and on V / M / σ / δ. Reports δ, V, M, θ and σ at that x. Not a support.
- σ
- Bending stress M / Zxx. Catalogue Z when the mill box is on. Indicative — not a member check.
- E
- Young’s modulus. Default 200 GPa for steel.
Supports (max 4)
Point loads (+down / −up)
UDL (+down / −up)
Elevation · elastic curve · query x = 3.00 m
Supports A pin @ 0.00 m · B roller @ 6.00 m. Grey line is the deflected shape (δ +up, down negative).
SHEAR V — kN
MOMENT M — kNm (sagging +)
STRESS σ — MPa (M / Zxx)
DEFLECTION δ — mm (+up, down −)
Simply supported · UDL w
Ra = Rb = wL / 2
M(x) = Ra x − w x² / 2 Mmax = w L² / 8 at mid-span
δ +up. Down is negative. δmax = −5 w L⁴ / 384 EI
V(x) = Ra − w x
Results
A pin @ 0.00 m Rv — kN24.0
B roller @ 6.00 m Rv — kN24.0
A θ — rad (deg)-0.0037 (-0.2°)
B θ — rad (deg)0.0037 (0.2°)
Mmax — kNm (sagging +)36.0
Vmax — kN-24.0
δ down — mm-6.88
δ up — mm0.00
|δ|peak — mm6.88
I used — 10⁶ mm⁴98.1
Zxx — 10³ mm³639.1
σ = Mmax/Z — MPa56.3
σ / fy (300 MPa)0.19
L/250 — mm24.0
L/300 — mm20.0
|δ|peak vs L/250OK
QUERY · AT x = 3.00 m
δ -6.88 mm · V -0.0 kN · M 36.0 kNmθ 0.0000 rad · 0.0° · σ 56.3 MPa
310UB46.2 · Ixx 98.1×10⁶ mm⁴ (fillets omitted) · fy 300 MPa. Mill tables govern.