HSS_Shape Example
See link below for the current HSS_Shapes from the AISC v16 steel database.
Constructing a HSS_Shape:
Before constructing, import the AISCSteel package. Also import the StructuralUnits package since we will use it later on.
using StructuralUnits
import AISCSteel
import AISCSteel.Shapes.HSS_Shapes as hssNow that the package has been imported, lets construct a HSS10x6x3/16.
hss_shape = hss.HSS_Shape("HSS10x6x3/16")AISCSteel.Shapes.HSS_Shapes.HSS_Shape("HSS10X6X3/16", 19.63 plf, 5.37 inch^2, 10.0 inch, 9.48 inch, 6.0 inch, 5.48 inch, 0.1875 inch, 0.174 inch, 74.6 inch^4, 18.0 inch^3, 14.9 inch^3, 3.73 inch, 34.1 inch^4, 12.7 inch^3, 11.4 inch^3, 2.52 inch, 73.8 inch^4, 19.9 inch^3, 29000.0 ksi, 50.0 ksi)The following went and searched through the AISC v16 steel database and pulled the relevant info to construct a HSS_Shape. You can now access information in the struct like so:
The overall width of the shape:
hss_shape.B6.0 inchThe weight of the HSS_Shape:
hss_shape.weight19.63 plfFlexure Capacity of HSS_Shape:
See link below for the available functions relating to flexure for the HSS_Shape member:
Major Axis Bending
We can calculate the flexural capacity about the x-axis of the HSS10x6x3/16 shape we just constructed:
L_b = 21ft
ϕ_b = 0.9
C_b = 1.14
M_nx = hss.Flexure.calc_Mnx(hss_shape, L_b, C_b)
ϕM_nx = ϕ_b * M_nx59.70594936286428 ft kipLets see what the calc_Mnx function did:
using Handcalcs
@handcalcs M_nx = hss.Flexure.calc_Mnx(hss_shape, L_b, C_b)\[\begin{aligned} \lambda &= \frac{b}{t} = \frac{5.48\;\mathrm{inch}}{0.174\;\mathrm{inch}} = 31.494252873563223 \\[10pt] \lambda_{p} &= 1.12 \cdot \sqrt{\frac{E}{F_{y}}} = 1.12 \cdot \sqrt{\frac{2.9 \cdot 10^{4}\;\mathrm{ksi}}{50\;\mathrm{ksi}}} = 26.973171856494744 \\[10pt] \lambda_{r} &= 1.4 \cdot \sqrt{\frac{E}{F_{y}}} = 1.4 \cdot \sqrt{\frac{2.9 \cdot 10^{4}\;\mathrm{ksi}}{50\;\mathrm{ksi}}} = 33.71646482061843 \\[10pt] \text{Since: }\lambda_{p} < \lambda \leq \lambda_{r} &= 26.973171856494744 < 31.494252873563223 \leq 33.71646482061843 = true \\[10pt] class &= noncompact \\[10pt] \lambda &= \frac{h}{t} = \frac{9.48\;\mathrm{inch}}{0.174\;\mathrm{inch}} = 54.48275862068966 \\[10pt] \lambda_{p} &= 2.42 \cdot \sqrt{\frac{E}{F_{y}}} = 2.42 \cdot \sqrt{\frac{2.9 \cdot 10^{4}\;\mathrm{ksi}}{50\;\mathrm{ksi}}} = 58.28131776135471 \\[10pt] \lambda_{r} &= 5.7 \cdot \sqrt{\frac{E}{F_{y}}} = 5.7 \cdot \sqrt{\frac{2.9 \cdot 10^{4}\;\mathrm{ksi}}{50\;\mathrm{ksi}}} = 137.27417819823216 \\[10pt] \text{Since: }\lambda \leq \lambda_{p} &= 54.48275862068966 \leq 58.28131776135471 = true \\[10pt] class &= compact \\[10pt] M_{p} &= F_{y} \cdot Z = 50\;\mathrm{ksi} \cdot 18\;\mathrm{inch}^{3} = 75\;\mathrm{ft}\,\mathrm{kip} \\[10pt] a_{w} &= \frac{2 \cdot h \cdot t_{w}}{b \cdot t_{f}} = \frac{2 \cdot 9.48\;\mathrm{inch} \cdot 0.174\;\mathrm{inch}}{5.48\;\mathrm{inch} \cdot 0.174\;\mathrm{inch}} = 3.4598540145985397 \\[10pt] h_{c} &= h = 9.48\;\mathrm{inch} \\[10pt] R_{pg} &= 1 - \frac{a_{w}}{1200 + 300 \cdot a_{w}} \cdot \left( \frac{h_{c}}{t_{w}} - 5.7 \cdot \sqrt{\frac{E}{F_{y}}} \right) = 1 - \frac{3.4598540145985397}{1200 + 300 \cdot 3.4598540145985397} \cdot \left( \frac{9.48\;\mathrm{inch}}{0.174\;\mathrm{inch}} - 5.7 \cdot \sqrt{\frac{2.9 \cdot 10^{4}\;\mathrm{ksi}}{50\;\mathrm{ksi}}} \right) = 1.127994562556279 \\[10pt] R_{pg} &= \mathrm{min}\left( R_{pg}, 1.0 \right) = \mathrm{min}\left( 1.127994562556279, 1.0 \right) = 1.0 \\[10pt] L_{p} &= \frac{0.13 \cdot E \cdot r_{y} \cdot \sqrt{J \cdot A_{g}}}{M_{p}} = \frac{0.13 \cdot 2.9 \cdot 10^{4}\;\mathrm{ksi} \cdot 2.52\;\mathrm{inch} \cdot \sqrt{73.8\;\mathrm{inch}^{4} \cdot 5.37\;\mathrm{inch}^{2}}}{75\;\mathrm{ft}\,\mathrm{kip}} = 17.51\;\mathrm{ft} \\[10pt] L_{r} &= \frac{2 \cdot E \cdot r_{y} \cdot \sqrt{J \cdot A_{g}}}{0.7 \cdot F_{y} \cdot S_{x}} = \frac{2 \cdot 2.9 \cdot 10^{4}\;\mathrm{ksi} \cdot 2.52\;\mathrm{inch} \cdot \sqrt{73.8\;\mathrm{inch}^{4} \cdot 5.37\;\mathrm{inch}^{2}}}{0.7 \cdot 50\;\mathrm{ksi} \cdot 14.9\;\mathrm{inch}^{3}} = 465\;\mathrm{ft} \\[10pt] M_{nFY} &= M_{p} = 75\;\mathrm{ft}\,\mathrm{kip} \\[10pt] \text{Since: }\lambda_{fclass} &= noncompact = true \\[10pt] M_{nFLB} &= M_{p} - \left( M_{p} - F_{y} \cdot S \right) \cdot \frac{\lambda_{f} - \lambda_{pf}}{\lambda_{rf} - \lambda_{pf}} = 75\;\mathrm{ft}\,\mathrm{kip} - \left( 75\;\mathrm{ft}\,\mathrm{kip} - 50\;\mathrm{ksi} \cdot 14.9\;\mathrm{inch}^{3} \right) \cdot \frac{31.494252873563223 - 26.973171856494744}{33.71646482061843 - 26.973171856494744} = 66.34\;\mathrm{ft}\,\mathrm{kip} \\[10pt] \text{Since: }\lambda_{wclass} &= compact = true \\[10pt] M_{nFLB} &= M_{p} = 75\;\mathrm{ft}\,\mathrm{kip} \\[10pt] \text{Since: }L_{p} < L_{b} \leq L_{r} &= 17.51\;\mathrm{ft} < 21\;\mathrm{ft} \leq 465\;\mathrm{ft} = true \\[10pt] M_{nLTB} &= C_{b} \cdot \left( M_{p} - \left( M_{p} - 0.7 \cdot F_{y} \cdot S_{x} \right) \cdot \frac{L_{b} - L_{p}}{L_{r} - L_{p}} \right) = 1.14 \cdot \left( 75\;\mathrm{ft}\,\mathrm{kip} - \left( 75\;\mathrm{ft}\,\mathrm{kip} - 0.7 \cdot 50\;\mathrm{ksi} \cdot 14.9\;\mathrm{inch}^{3} \right) \cdot \frac{21\;\mathrm{ft} - 17.51\;\mathrm{ft}}{465\;\mathrm{ft} - 17.51\;\mathrm{ft}} \right) = 85.22\;\mathrm{ft}\,\mathrm{kip} \\[10pt] M_{n} &= \mathrm{min}\left( M_{nY}, M_{nFLB}, M_{nWLB}, M_{nLTB} \right) = \mathrm{min}\left( 75\;\mathrm{ft}\,\mathrm{kip}, 66.34\;\mathrm{ft}\,\mathrm{kip}, 75\;\mathrm{ft}\,\mathrm{kip}, 85.22\;\mathrm{ft}\,\mathrm{kip} \right) = 66.34\;\mathrm{ft}\,\mathrm{kip} \end{aligned}\]
Minor Axis Bending
We can calculate the flexural capacity about the y-axis of the HSS10x6x3/16 shape we just constructed:
M_ny = hss.Flexure.calc_Mny(hss_shape)
ϕM_ny = ϕ_b * M_ny32.33912878030443 ft kipLets see what the calc_Mny function did:
@handcalcs M_ny = hss.Flexure.calc_Mny(hss_shape)\[\begin{aligned} \lambda &= \frac{b}{t} = \frac{9.48\;\mathrm{inch}}{0.174\;\mathrm{inch}} = 54.48275862068966 \\[10pt] \lambda_{p} &= 1.12 \cdot \sqrt{\frac{E}{F_{y}}} = 1.12 \cdot \sqrt{\frac{2.9 \cdot 10^{4}\;\mathrm{ksi}}{50\;\mathrm{ksi}}} = 26.973171856494744 \\[10pt] \lambda_{r} &= 1.4 \cdot \sqrt{\frac{E}{F_{y}}} = 1.4 \cdot \sqrt{\frac{2.9 \cdot 10^{4}\;\mathrm{ksi}}{50\;\mathrm{ksi}}} = 33.71646482061843 \\[10pt] \text{Since: }\lambda \leq \lambda_{p} &= 54.48275862068966 \leq 26.973171856494744 = false \\[10pt] \lambda_{p} < \lambda \leq \lambda_{r} &= 26.973171856494744 < 54.48275862068966 \leq 33.71646482061843 = false \\[10pt] class &= slender \\[10pt] \lambda &= \frac{h}{t} = \frac{5.48\;\mathrm{inch}}{0.174\;\mathrm{inch}} = 31.494252873563223 \\[10pt] \lambda_{p} &= 2.42 \cdot \sqrt{\frac{E}{F_{y}}} = 2.42 \cdot \sqrt{\frac{2.9 \cdot 10^{4}\;\mathrm{ksi}}{50\;\mathrm{ksi}}} = 58.28131776135471 \\[10pt] \lambda_{r} &= 5.7 \cdot \sqrt{\frac{E}{F_{y}}} = 5.7 \cdot \sqrt{\frac{2.9 \cdot 10^{4}\;\mathrm{ksi}}{50\;\mathrm{ksi}}} = 137.27417819823216 \\[10pt] \text{Since: }\lambda \leq \lambda_{p} &= 31.494252873563223 \leq 58.28131776135471 = true \\[10pt] class &= compact \\[10pt] M_{p} &= F_{y} \cdot Z = 50\;\mathrm{ksi} \cdot 12.7\;\mathrm{inch}^{3} = 52.92\;\mathrm{ft}\,\mathrm{kip} \\[10pt] a_{w} &= \frac{2 \cdot h \cdot t_{w}}{b \cdot t_{f}} = \frac{2 \cdot 5.48\;\mathrm{inch} \cdot 0.174\;\mathrm{inch}}{9.48\;\mathrm{inch} \cdot 0.174\;\mathrm{inch}} = 1.1561181434599157 \\[10pt] h_{c} &= h = 5.48\;\mathrm{inch} \\[10pt] R_{pg} &= 1 - \frac{a_{w}}{1200 + 300 \cdot a_{w}} \cdot \left( \frac{h_{c}}{t_{w}} - 5.7 \cdot \sqrt{\frac{E}{F_{y}}} \right) = 1 - \frac{1.1561181434599157}{1200 + 300 \cdot 1.1561181434599157} \cdot \left( \frac{5.48\;\mathrm{inch}}{0.174\;\mathrm{inch}} - 5.7 \cdot \sqrt{\frac{2.9 \cdot 10^{4}\;\mathrm{ksi}}{50\;\mathrm{ksi}}} \right) = 1.0790608279840679 \\[10pt] R_{pg} &= \mathrm{min}\left( R_{pg}, 1.0 \right) = \mathrm{min}\left( 1.0790608279840679, 1.0 \right) = 1.0 \\[10pt] M_{nFY} &= M_{p} = 52.92\;\mathrm{ft}\,\mathrm{kip} \\[10pt] \text{Since: }\lambda_{fclass} &= compact = slender = false \\[10pt] \lambda_{fclass} &= noncompact = slender = false \\[10pt] b_{e} &= 1.92 \cdot t_{f} \cdot \sqrt{\frac{E}{F_{y}}} \cdot \left( 1 - \frac{0.38}{\frac{b}{t_{f}}} \cdot \sqrt{\frac{E}{F_{y}}} \right) = 1.92 \cdot 0.174\;\mathrm{inch} \cdot \sqrt{\frac{2.9 \cdot 10^{4}\;\mathrm{ksi}}{50\;\mathrm{ksi}}} \cdot \left( 1 - \frac{0.38}{\frac{9.48\;\mathrm{inch}}{0.174\;\mathrm{inch}}} \cdot \sqrt{\frac{2.9 \cdot 10^{4}\;\mathrm{ksi}}{50\;\mathrm{ksi}}} \right) = 6.694\;\mathrm{inch} \\[10pt] b &= b - b_{e} = 9.48\;\mathrm{inch} - 6.694\;\mathrm{inch} = 2.786\;\mathrm{inch} \\[10pt] a &= b \cdot t_{f} = 2.786\;\mathrm{inch} \cdot 0.174\;\mathrm{inch} = 0.4847\;\mathrm{inch}^{2} \\[10pt] d &= \frac{Ht - t_{f}}{2} = \frac{6\;\mathrm{inch} - 0.174\;\mathrm{inch}}{2} = 2.913\;\mathrm{inch} \\[10pt] I_{e} &= I - 2 \cdot \left( \frac{b \cdot t_{f}^{3}}{12} + a \cdot d^{2} \right) = 34.1\;\mathrm{inch}^{4} - 2 \cdot \left( \frac{2.786\;\mathrm{inch} \cdot \left( 0.174\;\mathrm{inch} \right)^{3}}{12} + 0.4847\;\mathrm{inch}^{2} \cdot \left( 2.913\;\mathrm{inch} \right)^{2} \right) = 25.87\;\mathrm{inch}^{4} \\[10pt] S_{e} &= \frac{I_{e}}{\frac{Ht}{2}} = \frac{25.87\;\mathrm{inch}^{4}}{\frac{6\;\mathrm{inch}}{2}} = 8.624\;\mathrm{inch}^{3} \\[10pt] M_{nFLB} &= F_{y} \cdot S_{e} = 50\;\mathrm{ksi} \cdot 8.624\;\mathrm{inch}^{3} = 35.93\;\mathrm{ft}\,\mathrm{kip} \\[10pt] \text{Since: }\lambda_{wclass} &= compact = true \\[10pt] M_{nFLB} &= M_{p} = 52.92\;\mathrm{ft}\,\mathrm{kip} \\[10pt] M_{n} &= \mathrm{min}\left( M_{nY}, M_{nFLB}, M_{nWLB} \right) = \mathrm{min}\left( 52.92\;\mathrm{ft}\,\mathrm{kip}, 35.93\;\mathrm{ft}\,\mathrm{kip}, 52.92\;\mathrm{ft}\,\mathrm{kip} \right) = 35.93\;\mathrm{ft}\,\mathrm{kip} \end{aligned}\]