prying 9

"PRYING9" --- AISC 9th ED. PRYING ACTION ANALYSIS PROGRAM

Program Description:

"PRYING9" is a spreadsheet program written in MS-Excel for the purpose of analysis for prying action in

structural steel connections per the AISC 9th Edition (ASD) Code, pages 4-89 to 4-95. Specifically, bolt tension and

bolt shear are checked, and the prying force and required thickness are determined.

This program is a workbook consisting of three (3) worksheets, described as follows:

Worksheet Name DescriptionDoc This documentation sheet

Prying Action Prying action analysis for connections per AISC 9th Edition (ASD) Manual

Allowable Tension Force Allowable axial tension force at beam connection from bending due to prying

Program Assumptions and Limitations:

1. The Prying Action worksheet is valid for connections subjected to tension only, or to a combination of tension

and shear.

2. The Prying Action worksheet is only applicable for connection bolt diameters from 1/2” to 1-1/2 “

3. The Prying Action worksheet is only applicable for ASTM A325 or A490 high-strength connection bolts.

4. The Prying Action worksheet is applicable to connection bolts in bearing with threads included in shear plane

(N) or threads excluded from shear plane (X), as well as bolts in a slip critical connection (SC).

5. The Prying Action worksheet is applicable to connections with either standard or oversized bolt holes.

6. The Prying Action worksheet also takes fatigue effects into account when required to reduce the allowable bolt

tension stress.

7. The Allowable Tension Force worksheet has any applicable assumptions and limitations listed directly below

the tables of values.

8. This program contains numerous “comment boxes” which contain a wide variety of information including

explanations of input or output items, equations used, data tables, etc. (Note: presence of a “comment box”

is denoted by a “red triangle” in the upper right-hand corner of a cell. Merely move the mouse pointer to the

desired cell to view the contents of that particular "comment box".)

"PRYING9.xls" ProgramVersion 2.0

2 of 5 04/08/2023 16:10:09

PRYING ACTION ANALYSISFor Structural Steel Connections

Per AISC 9th Edition Manual (ASD) - Pages 4-89 to 4-95Job Name: Subject: ###

Job Number: Originator: Checker: ######

Input Data: ######

Total Tension Load, Tt = 53.70 kips bf/2=4.25 ###Total Shear Load, Vt = 26.80 kips g/2=2.75

Steel Yield, Fy = 36 ksi db=0.75 Q=2.94Bolt Diameter, db = 0.750 in. ###ASTM Bolt Desig. = A325 t=0.625

Bolt Type (N, X, or SC) = N A325Bolt Hole Type = Standard T+Q=11.89 A490

Tributary Length/Bolt, p = 4.500 in. tw=1.75 b'=1.5 a'=1.875 NTotal No. of Bolts, Nb = 6 bolts X

Width, bf = 8.5000 in. b=1.875 a=1.5 SCThickness, t = 0.6250 in. Standard

Thickness, tw = 1.7500 in. OversizedBolt Gage, g = 5.500 in. b =

No. of Loading Cycles = 20000 (for 25 years) b' =a =

Results: a' = 2*T=17.9

Check Bolt Tension and Shear: ###Ab = 0.4418 in.^2 Nomenclature N.A.vb = 4.47 kips/bolt vb = Vt/Nb d' =fv = 10.11 ksi fv = vb/AbT = 8.95 kips/bolt T = Tt/Nbft = 20.26 ksi ft = T/Ab

Tb = 28.00 kips Tb = Tb from AISC Table J3.7 (for A325 bolts) t(req'd) =Fv = 21.00 ksi Fv = Fv from AISC Table J3.2 (for N, X bolts)Vb = 9.30 kips/bolt Vb = Fv*Ab Vb >= vb, O.K. tc =

Ft(w/o Shr.) = 44.00 ksi Ft = (Ft from Table J3.2, fatigue is not considered)Ft = 38.56 ksi Ft = SQRT(Ft^2-(Ft/Fv)^2*fv^2) (for N, X bolts) Q =B = 17.00 kips/bolt B = Ft*Ab (for N, X bolts) B >= T, O.K. Check Allowable Bolt Tension with Prying Action:

Calculate Required Thickness: Ta =b = 1.8750 in. b = (g-tw)/2b' = 1.5000 in. b' = b-db/2a = 1.5000 in. a = minimum of: (bf-g)/2 or 1.25*b t(req'd) =a' = 1.8750 in. a' = a+db/2

0.8000d' = 0.8125 in. d' = dh = db+1/16 (for Standard holes)

0.81941.124

1.0000t(req'd) = 0.604 in. t >= t(req'd), O.K.

(continued)

r =

Ab = p*db^2/4

d =b = a' =

a =

a' =

r = r = b'/a'

d = d = 1-d'/pb = b = (1/r)*(B/T-1) a' = If b >= 1: a' = 1, If b < 1: a' = lesser of 1 or (1/d)*(b/(1-b))

t(req'd) = SQRT(8*T*b'/(p*Fy*(1+d*a')))

M2

M1

C9

This program assumes that the total tension load on the connection is concentrically applied to the bolt group, thus all bolts carry equal amount of tension. The total tension load MUST BE > 0!

C10

This program assumes that all bolts carry equal amount of shear. The total shear load MUST BE >= 0 !

C13

This program assumes the use of ONLY high-strength bolts of ASTM designation A325 or A490.

C14

This program assumes the following bolt type: N = Bearing bolt with threads included in shear plane X = Bearing bolt with threads excluded from shear plane SC = Slip-Critical bolt

C15

Bolt hole type may be either Standard or Oversized.

C16

The total Tributary Length/Bolt, p, is determined based on the type of connection as follows: 1. For "tee-stub" (WT), p = tributary length of flange, parallel to tee stem 2. For beam with clip angles, p = tributary length of angle, parallel to beam web 3. For beam with end-plate, p = tributary length of end-plate, parallel to beam web Note: 'p' is usually = bolt spacing, perpendicular to the bolt gage, 'g'. However, the minimum (critical) value of 'p' may be = (1/2 of bolt spacing + bolt edge distance).

C18

The total Width, bf, is determined based on the type of connection as follows: 1. For "tee-stub" (WT), bf = flange width of tee 2. For beam with clip angles, bf = [ 2*(angle leg length) + beam web thickness ] 3. For beam with end-plate, bf = width of end-plate

C19

The Thickness, t, is determined based on the type of connection as follows: 1. For "tee-stub" (WT), t = flange thickness of tee 2. For beam with clip angles, t = thickness of angle leg 3. For beam with end-plate, t = thickness of end-plate

C20

The total Thickness, tw, is determined based on the type of connection as follows: 1. For "tee-stub" (WT), tw = web thickness of tee 2. For beam with clip angles, tw = [ 2*(angle leg thk.) + beam web thickness ] 3. For beam with end-plate, tw = thickness of beam web

C21

The Bolt Gage, g, is the bolt spacing transverse to the tension load and parallel to connection width. Note: Typically this value is 5-1/2" for many connections.

C22

The Number of Loading Cycles reflects whether or not tensile fatigue is to be considered. When subject to tensile loading, the allowable tensile stress in A325 or A490 bolts due to the combined applied load and prying forces shall not exceed the values shown below, and the prying force shall not exceed 60% of the externally applied load. Tensile Fatigue (AISC Sect. A-K4) Ft (ksi) Ft (ksi) Number of Cycles A325 Bolts A490 Bolts <= 20,000* 44 54 20,000 to 500,000 40 49 > 500,000** 31 38 * approximately = to 2 applications/day for 25 years ** approximately = to 50 applications/day for 25 years Note: when the Number of Loading Cycles <= 20,000 then fatigue effects are ignored.

B27

Connection Bolt Data Nominal Diameter, d (in.) Area, Ab (in.^2) 1/2 0.1963 5/8 0.3068 3/4 0.4418 7/8 0.6013 1 0.7854 1-1/8 0.9940 1-1/4 1.2272 1-3/8 1.4850 1-1/2 1.7671

B32

TABLE J3.7 Minimum Pretension for Fully-tightened Bolts, kips* Bolt Size, in. A325 Bolts A490 Bolts 1/2 12 15 5/8 19 24 3/4 28 35 7/8 39 49 1 51 64 1-1/8 56 80 1-1/4 71 102 1-3/8 85 121 1-1/2 103 148 *Equal to 0.70 of minimum tensile strength of bolts, rounded off to nearest kip.

B33

TABLE J3.2 Allowable Stress on Fasteners, ksi Allowable Shear (Fv) Desription of Fasteners Slip-Critical Bearing-type Connections Connections Standard Oversized Holes Holes A325 bolts, when threads are 17.0 15.0 21.0 not excluded from shear planes A325 bolts, when threads are 17.0 15.0 30.0 excluded from shear planes A490 bolts, when threads are 21.0 18.0 28.0 not excluded from shear planes A490 bolts, when threads are 21.0 18.0 40.0 excluded from shear planes Notes: 1. For Slip-Critical connections, this program considers only standard or oversized holes. 2. Allowable shear stress values, 'Fv', shown above are for shear alone. 3. For Slip-Critical connections with combined tension and shear, the above values of 'Fv' shall be multiplied by the reduction factor: (1-ft*Ab/Tb).

I34

If Vb < vb, then either increase number of bolts (Nb), or increase bolt size/diameter (db).

B36

TABLE J3.2 Allowable Stress on Fasteners, ksi Desription of Fasteners Allowable Tension (Ft) A325 bolts, when threads are 44.0 not excluded from shear planes A325 bolts, when threads are 44.0 excluded from shear planes A490 bolts, when threads are 54.0 not excluded from shear planes A490 bolts, when threads are 54.0 excluded from shear planes Notes: 1. Allowable tension stress values shown above are for tension alone. 2. For Bearing-type connections with combined tension and shear, refer to Table J3.3 (below) for allowable tension stress values, 'Ft'. TABLE J3.3 Allowable Tension Stress, Ft, for Fasteners in Bearing-type Connections Description of Threads Included in Threads Excluded Fasteners Shear Plane from Shear Plane A325 bolts (44^2-4.39*fv^2)^1/2 (44^2-2.15*fv^2)^1/2 A490 bolts (54^2-3.75*fv^2)^1/2 (54^2-1.82*fv^2)^1/2 Note: above interaction equations are actually in the form of: Ft = (Ft^2-(Ft/Fv)^2*fv^2)^1/2

B37

Allowable Tension Load on Bolts (kips) ASTM Nominal Diameter, d (in.) Designation 1/2 5/8 3/4 7/8 1 1-1/8 1-1/4 1-3/8 1-1/2 A325 8.64 13.5 19.4 26.5 34.6 43.7 54.0 65.3 77.7 A490 10.6 16.6 23.9 32.5 42.4 53.7 66.3 80.2 95.4 Note: Values above are taken from AISC Table I-A, page 4-3, and are based on gross (nominal) area assuming NO shear.

I37

If B < T, then either increase number of bolts (Nb), or increase bolt size/diameter (db).

B45

Nominal Bolt Hole Dimensions (Table J3.1) Bolt Hole Dimensions (in.) Diameter Standard (Dia.) Oversized (Dia.) 1/2 9/16 5/8 5/8 11/16 13/16 3/4 13/16 15/16 7/8 15/16 1-1/16 1 1-1/16 1-1/4 >=1-1/8 d+1/16 d+5/16

B46

d = Ratio of net area (at bolt line) and the gross area (at the face of the stem or angle leg).

B48

a ' = Value of a for which required thickness, t(req'd), is a minimum or allowable applied tension per bolt, Ta, is a maximum.

I49

If t < t(req'd), then either increase thickness (t), increase number of bolts (Nb), decrease bolt gage (g), increase bolt size/diameter (db), or increase tributary clip angle length/bolt (p) by increasing bolt vertical spacing (S).


3 of 5 04/08/2023 16:10:09

Calculate Prying Force, Q:

1.122 in. tc = SQRT(8*B*b'/(p*Fy)) (to develop 'B' in bolts/no prying)0.851

Q = 2.94 kips

Check Allowable Bolt Tension with Prying Action:

1.5076Ta = 9.59 kips

Ta >= T, O.K.Calculate Required Thickness to Eliminate Prying Action:

0.814 in.

Comments:

tc =a = a = 1/d*((T/B)/(t/tc)^2-1) (Note: 0 <= a <= 1.0)

Q = B*d*a*r*(t/tc)^2 (prying force per bolt at design load)

a' = a' = 1/(d*(1+r))*((tc/t)^2-1)If a' >1: Ta = B*(t/tc)^2*(1+d) , If a' < 0: Ta = BIf 0 <= a' <= 1: Ta = B*(t/tc)^2*(1+d*a')

t(req'd) = t(req'd) = SQRT(8*T*b'/(p*Fy))

B55

tc = Flange or angle thickness required to develop 'B' in bolts with no prying action.

B56

a = Ratio of moment at bolt line to moment at stem line. = M2/(d*M1). where: M1 = M2 = T*b/2

I64

If Ta < T, then either increase thickness (t), increase number of bolts (Nb), decrease bolt gage (g), increase bolt size/diameter (db), or increase tributary length/bolt (p) by increasing bolt vertical spacing (S).


4 of 5 04/08/2023 16:10:09

PRYING ACTION ANALYSISAllowable Axial Tension Force at Beam End Connection

Based on Bending in Clip Angles or End Plate Due to Prying ActionJob Name: Subject: ###

Job Number: Originator: Checker: ######

Input Data: ### bf=8+tw bf=8 ###

Steel Yield (Clips/Plate), Fy = 36 ksi g=5.5 g=5.5 ###Bolt Diameter, db = 0.750 in. t t ###ASTM Bolt Desig. = A325 Nr Nr ###

Bolt Type (N, X, or SC) = N 3 T 3 T ###Bolt Hole Type = Standard 3 3 ###

Tributary Length/Bolt, p = 2.750 in. A325Bolt Gage, g = 5.500 in. Lc=4 tw tw A490

NFor End Plate

5/16 3/8 1/2 5/8 3/4 1/2 5/8 3/4 1ALLOWABLE AXIAL TENSION FORCE AT BEAM END CONNECTION (kips)

Beam Beam # Bolt t = 5/16'' t = 3/8" t = 1/2" t = 5/8" t = 3/4" t = 1/2" t = 5/8" t = 3/4" t = 1"Size Web, tw Rows Clip Clip Clip Clip Clip End End End End

(Depth) (in.) (Nr) Angles Angles Angles Angles Angles Plate Plate Plate PlateW6 0.170 1 2.1 3.1 5.9 9.9 15.4 4.6 7.2 10.4 18.4W8 0.170 2 4.2 6.2 11.8 19.8 30.8 9.2 14.4 20.7 36.8

W10 0.190 2 4.2 6.2 11.9 19.9 31.0 9.3 14.5 20.8 37.0

W12 0.2002 4.2 6.2 11.9 20.0 31.1 8.9 14.5 20.9 37.13 6.3 9.4 17.8 30.0 46.7 13.9 21.7 31.3 55.6

W14 0.230 3 6.3 9.4 18.0 30.2 47.1 14.0 21.9 31.5 56.0

W16 0.2503 6.4 9.5 18.1 30.4 47.5 14.1 22.0 31.6 56.34 8.5 12.7 24.1 40.6 63.3 18.8 29.3 42.2 75.0

W18 0.3003 6.5 9.6 18.3 30.9 48.3 14.2 22.2 32.0 56.94 8.6 12.8 24.5 41.2 64.4 19.0 29.6 42.7 75.85 10.8 16.0 30.6 51.5 80.4 23.7 37.0 53.3 94.8

W21 0.3504 8.7 13.0 24.8 41.9 65.5 19.2 30.0 43.1 76.75 10.9 16.3 31.0 52.3 81.8 24.0 37.5 53.9 95.96 13.1 19.5 37.2 62.8 98.2 28.8 44.9 64.7 115.1

W24 0.3955 11.0 16.5 31.4 53.1 83.1 24.2 37.8 54.5 96.96 13.3 19.7 37.7 63.7 99.7 29.1 45.4 65.4 116.27 15.5 23.0 44.0 74.3 116.4 33.9 53.0 76.3 135.6

W27 0.460

5 11.2 16.8 32.1 54.2 85.1 24.6 38.4 55.3 98.36 13.5 20.1 38.5 65.1 102.1 29.5 46.1 66.4 118.07 15.7 23.5 44.9 75.9 119.1 34.4 53.8 77.4 137.78 18.0 26.8 51.3 86.7 136.1 39.3 61.5 88.5 157.3

W30 0.470

6 13.5 20.2 38.6 65.3 102.4 29.6 46.2 66.5 118.37 15.8 23.5 45.0 76.1 119.5 34.5 53.9 77.6 138.08 18.0 26.9 51.4 87.0 136.6 39.4 61.6 88.7 157.79 20.3 30.3 57.9 97.9 153.7 44.4 69.3 99.8 177.4

W33 0.550

6 13.8 20.6 39.6 67.0 105.5 30.1 47.1 67.8 120.57 16.1 24.1 46.1 78.2 123.0 35.2 54.9 79.1 140.68 18.4 27.5 52.7 89.4 140.6 40.2 62.8 90.4 160.79 20.7 31.0 59.3 100.6 158.2 45.2 70.6 101.7 180.8

10 23.0 34.4 65.9 111.7 175.8 50.2 78.5 113.0 200.9

W36 0.600

6 14.0 20.9 40.2 68.2 107.5 30.5 47.7 68.6 122.07 16.4 24.4 46.9 79.6 125.4 35.6 55.6 80.1 142.38 18.7 27.9 53.6 90.9 143.3 40.7 63.5 91.5 162.79 21.0 31.4 60.3 102.3 161.2 45.7 71.5 102.9 183.0

10 23.4 34.9 67.0 113.7 179.1 50.8 79.4 114.4 203.3

For Clip Angles

B20

Inputting the minimum value of a beam web thickness (tw) for a particular beam size (depth) will result in a conservative value calculated for the allowable tension force at beam end connection.

C20

Number of Rows of Bolts: W8 - 2 W10 - 2 W12 - 2, 3 W14 - 3 W16 - 3, 4 W18 - 3, 4, 5 W21 - 4, 5, 6 W24 - 5, 6, 7 W27 - 5, 6, 7 W30 - 6, 7, 8 W33 - 6, 7, 8, 9 W36 - 6, 7, 8, 9, 10


5 of 5 04/08/2023 16:10:09

a' =

Notes:T =

1. Primary use of this table is to quickly determine if clip angles or end plate connection should be used. W36x256

2. For double-angle clips, this table assumes 2-L4x3-1/2 angles with long outstanding legs (OSL). For 3/4" Clip Angles:3. Total width for double-angle clip connection, bf = 2*4" + min. beam web thickness (tw) = 8"+tw. Beam Size:4. Total width of end plate is assumed to be bf = 8". Nb =5. This table is for axial tension force (transfer force at joint) only. Beam end shear is not considered. bf =6. Check of combined stresses on connection bolts must be done independently. b =7. Forces shown in table are conservative, when based on use of minimum web thickness for given beam size (depth). b' =8. Forces shown in table are "unfactored", i.e., allowable stress increases for wind or seismic are not included. a =

a' =Prying Action Analysis Formulas:

tc =Nb = 2*Nrbf = 2*(4" OSL)+tw , for clip angles T =bf = 8" , for end plate W33x515

b = (g-(2*ta+tw))/2 , for clip angles For 1/2" End Plate:b = (g-tw)/2 , for end plate Beam Size:b' = b-db/2 Nb =a = minimum of: (bf-g)/2 or 1.25*b bf =a' = a+db/2 b =

b' =B = 19.44 kips/bolt (for 0.75" A325N bolts) a =d' = dh = 0.8125 (for Standard bolt holes) a' =

tc = SQRT(8*B*b'/(p*Fy)) tc =

T =Allowable axial tension force, T: W33x141

For 5/8" End Plate:Beam Size:

Nb =bf =b =b' =a =a' =

tc =

T =W30x211

For 3/4" End Plate:Beam Size:

Nb =bf =b =b' =a =a' =

tc =

T =

r =

a' =

r =

a' =

r = b'/a'

d = 1-d'/p r =

a' = 1/(d*(1+r))*((tc/t)^2-1) a' =

If a' > 1 , T = Nb*(B*(t/tc)^2*(1+d)) If 0 <= a' <= 1 , T = Nb*(B*(t/tc)^2*(1+d*a')) If a' < 0 , T = Nb*B

r =

a' =

r =

a' =

prying 9

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