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Non-Composite - UnreinforcedProject:Project No.:Date:Subject:Steel Beam with Web PenetrationBy:G.F. SheaOpening Not ReinforcedPage:

This worksheet determines the Allowable Moment and Shear for a known steel beam size with a given web opening.Cells requiring data input are highlighted in yellow.Source: AISC Steel Design Guide 2, Steel and Composite Beams with Web Openings; 1990Validation:Example 1, Steel Beam with Unreinforced Opening, from Source documentMember Data:Beam Size:W8x21depth:d =8.3inflange width:bf =5.27inflange thickness:tf =0.400inweb thickness:tw =0.250inPlastic Section Modulus:Zx =20.4in3Yield Stress:Fy =50.0ksiHole Parameters:Rectangular Hole:ORCircular Hole:Height (in):h =4.5Diameter (in):D =Length (in):l =4Rectangular openings are required to have radiused cornersNote: The Design Guide treats circular holes Radius =0.625inERROR:#NAME?as equivalent rectangular holesho =4.5ERROR:#NAME?ao =4ERROR:#NAME?ao/ho =0.8888888889ERROR:#NAME?po =4.15ERROR:#NAME?

Location of Opening:h2 =5.25inCenterline of opening from bottom of beam (in):st =0.78inERROR:#NAME?sb =3.00inERROR:#NAME?vt =5.13ERROR:#NAME?vb =1.33ERROR:#NAME?e =-1.11inERROR:#NAME?

Openings must be located so that the edge of the opening is not closer than distance d to the beam endOpenings must be located so that the edge of an opening is not closer than distance d to a point load

Proportioning and Detailing Guidelines, Table 4.5:Beam Dimensions and Limits on Vm:Width to thickness ratio of flanges:Opening Dimensions:ratio1 =6.6ERROR:#NAME?ao/ho_max =3.0ERROR:#NAME?Limit1 =9.2ERROR:#NAME?ho_max =5.796inERROR:#NAME?Width to thickness ratio of web:po_max =5.6ratio2 =29.9ERROR:#NAME?Tee Dimensions:Limit2A =73.5ERROR:#NAME?st_min =1.242inERROR:#NAME?Limit2B =59.4ERROR:#NAME?sb_min =1.242inERROR:#NAME?

Determine Maximum Moment Capacity (Mm):The nominal moment capacity of a beam with openings is a portion of the design flexural strength of a beam without openings. For a single span beam with a deck attached the design flexural strength Mn equals the plastic moment Mp which is equal to Fy*Zx. Mp =85k-ftERROR:#NAME?1020k-inAs =1.125in2ERROR:#NAME?Mm =ERROR:#NAME?k-ftERROR:#NAME?b =0.9Mm =ERROR:#NAME?k-ftERROR:#NAME?k-in

Determine Maximum Shear Capacity:Vp =59.76kERROR:#NAME?Vpb =21.65kERROR:#NAME?vb =0.799ERROR:#NAME?Vmb =17.3006077383kERROR:#NAME?Vpt =5.63kERROR:#NAME?In the table below the input values for Points 1 through 6 are taken from table 4.6 of the Reference Document.vt =0.357ERROR:#NAME?The Min and Max values were obtained using the worksheet BEMANL, which can be found on the XLC Repository.Vmt =2.01kERROR:#NAME?Vn, Mn and R are calculated using the formulas shown on the adjacent page.Vm =19.31kERROR:#NAME?Closest location to beam end based on minimum end clearanceVm_max =39.84kERROR:#NAME?v =0.9Farthest distance from left based on R 1.00Vm =17.38kERROR:#NAME?Interpretation of Table 4.6, Allowable Locations for Openings, Example 1Determine Moment-Shear Interaction:Point =Min1234Max56x =6ftDistance from left support to centerline of openingX =2.833.006.009.0012.0014.515.0018.00Mu =500.00k-ftMu =94.2599.33180.75244.00289.17313.00316.25325.25Vu =0.01k(Note that the shear value is actually 0, but this gives a division by 0 error)Vu =30.4630.124.118.112.007.036.000.01Vn =ERROR:#NAME?ERROR:#NAME?ERROR:#NAME?ERROR:#NAME?ERROR:#NAME?ERROR:#NAME?ERROR:#NAME?ERROR:#NAME?Vn =ERROR:#NAME?kERROR:#NAME?Mn =ERROR:#NAME?ERROR:#NAME?ERROR:#NAME?ERROR:#NAME?ERROR:#NAME?ERROR:#NAME?ERROR:#NAME?ERROR:#NAME?R =ERROR:#NAME?ERROR:#NAME?ERROR:#NAME?ERROR:#NAME?ERROR:#NAME?ERROR:#NAME?ERROR:#NAME?ERROR:#NAME?Mn =ERROR:#NAME?k-ftERROR:#NAME?From the table above it can be seen that the centerline of the opening can be placed between a point 2.83 feet from the support and a point 14.5 feet from the support.R =ERROR:#NAME?ERROR:#NAME?Note: If R > 1.0, reinforcement must be added or the opening needs to be moved. See following Tab.See table on adjacent page for determination of allowable opening locations.

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Non-Composite - ReinforcedProject:Project No.:Date:Subject:Steel Beam with Web PenetrationBy:G.F. SheaReinforcement AddedPage:

This worksheet determines Required Reinforcement for a steel beam with known Moment and Shear and a required web ERROR:#NAME?opening at a given location. Cells requiring data input are highlighted in yellow.Source: AISC Steel Design Guide 2, Steel and Composite Beams with Web Openings; 1990Validation: Example 2, Steel Beam with Reinforced Opening, from source documentMember Data:Beam Size:W18X55depth:d =18.1inflange width:bf =7.53inflange thickness:tf =0.630inweb thickness:tw =0.390inPlastic Section Modulus:Zx =112.0in3Yield Stress:Fy =50.0ksiHole Parameters:Rectangular Hole:ORCircular Hole:Height (in):h =11Diameter (in):D =Length (in):l =20Rectangular openings are required to have radiused cornersNote: The Design Guide treats circular holes Radius_min =0.78inERROR:#NAME?as equivalent rectangular holes

ho =11ERROR:#NAME?ao =20ERROR:#NAME?ao/ho =1.82ERROR:#NAME?po =5.46ERROR:#NAME?

Location of Opening:h2 =9.05inCenterline of opening from bottom of beam (in):st =3.55inERROR:#NAME?sb =3.55inERROR:#NAME?vt =5.63ERROR:#NAME?vb =5.63ERROR:#NAME?e =0.00inERROR:#NAME?

Openings must be located so that the edge of the opening is not closer than distance d to the beam endOpenings must be located so that the edge of an opening is not closer than distance d to a point load

Proportioning and Detailing Guidelines, Table 4.5:Beam Dimensions and Limits on Vm:Width to thickness ratio of flanges:Opening Dimensions:ratio1 =6.0ERROR:#NAME?ao/ho_max =3.0ERROR:#NAME?Limit1 =9.2ERROR:#NAME?ho_max =12.67inERROR:#NAME?Width to thickness ratio of web:po_max =5.6ratio2 =43.2ERROR:#NAME?Tee Dimensions:Limit2A =73.5ERROR:#NAME?st_min =2.715inLimit2B =59.4ERROR:#NAME?sb_min =2.715inERROR:#NAME?Determine Maximum Moment Capacity (Mm):The nominal moment capacity of a beam with openings is a portion of the design flexural strength of a beam without openings. For a single span beam with a deck attached the design flexural strength Mn equals the plastic moment Mp which is equal to Fy*Zx.

Mp =466.6666666667k-ftERROR:#NAME?5600k-inAs =4.29in2ERROR:#NAME?Mm =ERROR:#NAME?k-ftERROR:#NAME?b =0.9Mm =ERROR:#NAME?k-ftERROR:#NAME?ERROR:#NAME?k-in

Determine Maximum Shear Capacity:Vp =203.78kERROR:#NAME?Vpb =39.97kERROR:#NAME?vb =0.333ERROR:#NAME?Vmb =13.29kERROR:#NAME?Vpt =39.97kERROR:#NAME?vt =0.333ERROR:#NAME?Vmt =13.29kERROR:#NAME?Vm =26.58kERROR:#NAME?Vm_max =135.85kERROR:#NAME?v =0.9Vm =23.92kERROR:#NAME?Determine Moment-Shear Interaction:x =ftDistance from left support to centerline of openingMu =300.00k-ftVu =30kVn =ERROR:#NAME?kERROR:#NAME?Mn =ERROR:#NAME?k-ftERROR:#NAME?R =ERROR:#NAME?ERROR:#NAME?Note: If R > 1.0, reinforcement must be added. See following Page.From Design Example 2, page 26: "Reinforcement should be selected to reduce R to 1.0. Since the reinforcement willincrease Mm of a steel member only slightly, the increase in strength will be obtained primarily through the effect ofthe reinforcement on the shear capacity, Vm.Ar_max =2.25in2ERROR:#NAME?Max. reinforcement area if bars added to both sides of webIf reinforcing bars are used on only one side of the beam web, the section should meet the following additional checks and requirements:Check 1: a0/h0 2.5C1 =OKCheck 2:st/tw 140/sqrt(Fy)C2 =OKCheck 3:sb/tw 140/sqrt(Fy)C3 =OKCheck 4:Mu/Vud 20C4 =OKNo. of sides of web requiring reinforcement:1Requirement 5:Ar Af/3Af =4.74in2ERROR:#NAME?ERROR:#NAME?Flange AreaAr1_max =1.58in2ERROR:#NAME?Maximum Reinforment Areatr_min =0.25inBased on 3/16" fillet weld (E70XX) top and bottomtr_max =0.630inERROR:#NAME?br_max =6.33inERROR:#NAME?Maximum reinforcing widthbr_max2 =3.57inERROR:#NAME?Width limited so reinforcing will not protrude beyond beam flangeAs a practical matter, assume the smallest reinforcement bar that can be used is 0.25" x 1.5"tr =0.375inUse 1/8" incrementsbr =1.75inUse 1/4" incrementsAr =0.66in2ERROR:#NAME?Proposed Reinforcement AreaERROR:#NAME?

Pr =32.813kipsERROR:#NAME?Force in Reinforcement along edge of openingstr =3.506inERROR:#NAME?vtr =5.704ERROR:#NAME?dtr =3.363inERROR:#NAME?sbr =3.506inERROR:#NAME?vbr =5.704ERROR:#NAME?dbr =3.363inERROR:#NAME?

Determine Maximum Shear Capacity:br =1.56ERROR:#NAME?vbr =0.539ERROR:#NAME?Vmbr =21.53kipsERROR:#NAME?tr =1.56ERROR:#NAME?vtr =0.539ERROR:#NAME?ERROR:#NAME?Vmtr =21.53kERROR:#NAME?Vmr =43.05kERROR:#NAME?ERROR:#NAME?Vmr_max =135.85kERROR:#NAME?v =0.9Vmr =38.75kERROR:#NAME?Determine Maximum Moment Capacity:Mmr =ERROR:#NAME?k-ftERROR:#NAME?

Mmr =ERROR:#NAME?k-ftERROR:#NAME?k-inCheck Interaction:Rr =ERROR:#NAME?ERROR:#NAME?Reinforcement Weld Requirements:Fyr =50ksiYield stress of reinforcement should match beamRwr =59.1kERROR:#NAME?Required strength of weld within the length of openingRwre =29.6kERROR:#NAME?Required strength of the weld within each extensionle =5inERROR:#NAME?Reinforcement extension beyond opening - each sideLr =30inERROR:#NAME?Overall length of reinforcementDr =3/16 inERROR:#NAME?Weld size on one side of reinforcement at openingDre =3/16 inERROR:#NAME?Weld size on both sides of reinforcement at extension

Summary of Reinforcement Requirements:Thickness =0.375inWidth =1.75inLength =30inInstall on 1 side of webWeld one side at opening =3/16 incontinuousWeld both sides at extension =3/16 incontinuous

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Steel Data 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