Tensile Strength and Capacity Control of the W-Shape Sections According to AISC 360-16

IntroductionThis calculator prepared to calculate the Tension Yielding and Rupture strength of the W-Shape members that fastened by bolts according to AISC 360-16. The main purpose of this study to get the tension capacity values without the using of the Design Tables that shared by AISC. User can calculate the capacities and also check the demand to capacity ratios if they have design forces. Also, the behind the calculation of the capacity can be understandable with this way.
❗ This calculation has been written in accordance with AISC 360:16. 
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Typical view of the W-Shape section (Source: AISC 360-16 Design Examples)
To calculate the tensile rupture strength of the W-Shape sections, the fasteners such as bolts has to be considered in the calculation to get the gross and net area ratio. If the ratio lower than the 0.75, tensile rupture has to be calculated by formula! Because of that, the Design Table values will be unacceptable. 
The user has to be define the bolt diameters, numbers and distance between the bolts if the considered fasteners affect on the section.
📃 List of symbols used in this calculator
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Design Method = LRFD or ASD for the load factors\footnotesize{\text{Design\ Method = LRFD\ or\ ASD\ for\ the\ load\ factors}}Design Method = LRFD or ASD for the load factors
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Length = The total length of the section (ft)\footnotesize{\text{Length\ = The\ total\ length\ of\ the\ section\ (ft)}}Length = The total length of the section (ft)
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Fy=Yielding strength of the steel(ksi)\footnotesize{F_y = \text{Yielding\ strength\ of\ the\ steel}\hspace{0.1cm}(ksi)}Fy​=Yielding strength of the steel(ksi)
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Fu=Ultimate yielding strength of the steel(ksi)\footnotesize{F_u = \text{Ultimate\ yielding\ strength\ of\ the\ steel}\hspace{0.1cm}(ksi)}Fu​=Ultimate yielding strength of the steel(ksi)
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PG=Design tension force for gravity load(kips)\footnotesize{P_G = \text{Design\ tension\ force\ for\ gravity\ load}\hspace{0.1cm}(kips)}PG​=Design tension force for gravity load(kips)
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PQ=Design tension force for live load(kips)\footnotesize{P_Q = \text{Design\ tension\ force\ for\ live\ load}\hspace{0.1cm}(kips)}PQ​=Design tension force for live load(kips)
CalculationTechnical notes
This work only calculating the Tension Yielding Capacity and Tensile Rupture Strength of the W-Shape members according to AISC 360:16
To get the capacities and demand to capacity ratio of the any W-Shape section, you can just use the Inputs! The results will be seen in the Outputs part.
⬇️ InputsSection and Design Properties
﻿﻿Section
:W10X22​
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﻿﻿Design Method
:LRFD​
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﻿﻿Length
:25.00ft​
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Material Properties
﻿﻿Fy
:70.0​
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﻿﻿Fu
:90.0​
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Design Forces
﻿﻿PG
:100kips​
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﻿﻿PQ
:90kips​
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Bolted Connection
﻿﻿Diameter of Bolt
:0.75in​
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﻿﻿# of Bolts
:6​
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﻿﻿Distance Between Bolts
:3in​
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⬆️ OutputsCapacities
﻿﻿Td
:288.351kips​
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﻿﻿Tn
:408.87kips​
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Demand to Capacity Ratio
﻿﻿Ratio
:0.915550839081536​
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Slenderness Check
﻿﻿Result
:OK​
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⬆️ Tensile Strength ChecksExplanationIn this chapter, we just focused to pure tension capacity and demand to capacity ratio (DCR) of the W-Shape sections according to AISC 360-16.
To calculate the tension yielding/rupture strength of the member, the section properties has to be available such as gross area, width, depth, thickness (flange and web).
To calculate the capacity and DCR of the section user has to define Design Method, length of the section and steel grades for yielding and rupture.
Design methods can be defines as LRFD and ASD, steel grades should be selected as according to project or related calculation properties.
The other important thing about the tension rupture capacity of the section is the section fastened via bolts or welds. In this study we just focused to the bolted connection. 
If the section has a connection (bolt connection) the user should be defined the diameter of bolt, distance between bolts and the number of the bolts. It will be affected directly the calculation of the tensile rupture strength of the section.
The difference of this study from the design manual, all of calculation can be done quickly and also tensile rupture strength can be seen except from the design manual. Because the design manual does not have the Td value if the Ae/Ag less than 0.75.
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Tensile Yielding Strength calculation according to AISC 360-16.
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Tensile Rupture Strength calculation according to AISC 360-16.
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Schematic view of the W Section with the bolt holes
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