lrfd design spreadsheet

Tensile Rupture (Sections D2 & J4.1b) Pn = AeFu = AnUFu

Fu = 58ksi Ag = 4.5in2 tpl = 0.5in # members 1

db = 0.75in Connecting Element? N (Y or N)

Net Area Determination failure path #1

s g s2/4g Total width tpl Area (in) (in) (in) (in) (in2) width segment 1 0.000 1.500 0.000 1.500 0.500 0.750 width segment 2 0.000 3.000 0.000 3.000 0.500 1.500 width segment 3 0.000 3.000 0.000 3.000 0.500 1.500 width segment 4 0.000 1.500 0.000 1.500 0.500 0.750 hole 1 -0.875 0.500 -0.438 hole 2 -0.875 0.500 -0.438 hole 3 0.000 0.500 0.000 Net Area 3.625 failure path #2

s g s2/4g Total width tpl Area (in) (in) (in) (in) (in2) width segment 1 0.000 1.500 0.000 1.500 0.500 0.750 width segment 2 3.000 3.000 0.750 3.750 0.500 1.875 width segment 3 3.000 3.000 0.750 3.750 0.500 1.875 width segment 4 0.000 1.500 0.000 1.500 0.500 0.750 hole 1 -0.875 0.500 -0.438 hole 2 -0.875 0.500 -0.438 hole 3 -0.875 0.500 -0.438 Net Area 3.938

0.85Ag = 3.825in2

Controlling An = 3.625in2 U = 1.000

Ae = 3.625in2

Pn = 210.3kips Determine Capacity LRFD ASD

t = 0.75 t = 2

t Pn = 158kips Pn / t = 105kips CLF 1.40 CLF 0.90

Ps,eq = 112.6kips Ps,eq = 116.8kips Check Capacity LRFD ASD

t = 0.75 t = 2 t Pn = 158kips Pn / t = 105kips Pu 50.00kips Pa 35.00kips Pu/tPn = 31.7%kips Pa / (Pn / t ) = 33.3%kips Okay Okay

Tensile Yielding (Sections D2 & J4.1a) Pn = AgFy

Ag 2in2 Fy = 50ksi Pn = 100kips

IF you need to determine capacity: LRFD ASD

t = 0.9 t = 1.67 t Pn = 90kips Pn / t = 60kips

CLF 1.40 CLF 0.90 Ps,eq = 64.3kips Ps,eq = 66.5kips

IF you need to check capacity: LRFD ASD

t = 0.9 t = 1.67 t Pn = 90kips Pn / t = 60kips Pu 50.00kips Pa 35.00kips Pu/tPn = 55.6%kips Pa / (Pn / t ) = 58.5%kips

Okay Okay

Bolt Bearing (J3.10)

deformation at bolt hole IS a design consideration: Rn = min[1.2LctFu, 2.4dtFu] deformation at bolt hole IS NOT a design consideration: Rn = min[1.5LctFu, 3.0dtFu] long slotted holes perpendicular to force: Rn = min[1.0LctFu, 2.0dtFu]

Deformation at the bolt hole is not a design consideration Use Equation J3-6b

tpl = 0.5in End dist 1.5in db = 0.75in Lc = 1.0625in

Fu = 65ksi num bolts 12bolts/connection Tear Bearing Use Use Out Deformation (k/bolt) (k/bolt) (k/bolt) (k)

Fu factor 1.5 3.0 Rn 51.8 73.1 51.8 621.6

Controlling Rn = 621.6k

IF you need to determine capacity: LRFD ASD

t = 0.75 t = 2 t Pn = 466kips Pn / t = 311kips


IF you need to check capacity: LRFD ASD

t = 0.75 t = 2 t Pn = 466kips Pn / t = 311kips Pu 50.00kips Pa 50.00kips Pu/tPn = 10.7%kips Pa / (Pn / t ) = 16.1%kips

Okay Okay

Block Shear (Section J4.3) Rn = min[0.6FuAnv + UbsFuAnt, 0.6FyAgv + UbsFuAnt] Fy = 36ksi Fu = 58ksi tpl = 1in db = 0.75in

Failure Path #1 gross path number net path length holes/path length # paths Area (in) (in) (in^2)

Agv 10.500 0.000 10.500 2.000 21.000 Anv1 10.500 3.500 7.438 1.000 7.438

Anv2 10.500 3.500 7.438 1.000 5.578 Ant 6.000 1.000 5.125 1.000 5.125

Ubs 1.0

Shear Shear Use Fracture Yield (k) (k) (k)

Rn 750.2 750.9 750.2 Failure Path #2 gross path number net path length holes/path length # paths Area (in) (in) (in^2)

Agv 10.500 0.000 10.500 1.000 10.500 Anv 10.500 3.500 7.438 1.000 7.438 Ant 7.500 1.500 6.188 1.000 6.188

Ubs 0.5

Shear Shear Use Fracture Yield (k) (k) (k)

Rn 438.3 406.2 406.2

Controlling Rn = 406.2k IF you need to determine capacity: LRFD ASD

t = 0.75 t = 2 t Pn = 305kips Pn / t = 203kips


If you need to check capacity: LRFD ASD

t = 0.75 t = 2 t Pn = 305kips Pn / t = 203kips Pu 50.00kips Pa 50.00kips Pu/tPn = 16.4%kips Pa / (Pn / t ) = 24.6%kips

Okay Okay

Tension Limit State SummaryLast Revised:

Serviceability Limit States:

Limit State Specification Limit

Slenderness D1L/r < 300

orr > L/300

Strength Limit States:

All strength limit states take the form:

LRFD ASDPu < tPn Pa < Pn/t

Req'd Pn = Pu/t < Pn Req'd Pn = Pa t < Pn

Pu / (tPn) < 1.00 Pa / (Pn/t) < 1.00

Rn (nominal resistance) is often used in place of Pn (nominal axial strength) in the equations above.

Limit State

Specification Nominal Capacity

Typical Design

Variables

Tensile Yielding D2(a)/J4.1(a)

Member Capacity:

FyAg

Stl Type, Section 0.90 1.67

Tensile Rupture D2(b)/J4.1(b)

Member Capacity:

FuAe

Stl Type, Section, Bolt size,

Bolt Layout, Section

modifications

0.75 2.00

Block Shear

J4.3 Capacity per connection:

min(0.6FuAnv +

Stl Type, Section, Bolt Size,

Bolt Layout,

0.75 2.00

UbsFuAnt, 0.6FyAgv + UbsFuAnt)

Section modificatio

ns

Bolt Bearing J3.10

Capacity per bolt hole:

Std Holes, Defl an issue:

min(1.2 Lct Fu, 2.4 dt Fu)

Std Holes, Defl not issue:

min(1.5 Lct Fu, 3.0 dt Fu)

Stl Type, Section, Bolt Size,

Bolt Layout, Section

modifications

0.75 2.00

Notes:

1. See SCM specification D3 for requirements for computing An, and Ae.

2. SCM specification J4.1(b) places an upper limit of 0.85Ag on An for connecting elements.

3. Multiple failure paths may need to be considered for Tensile Rupture and Block Shear.

4. The least bolt bearing value in a connection controls the bolt bearing strength of the member.

Bolt SummaryLast Revised:

Strength Limit States:

All strength limit states take the form:

LRFD ASDRu < tRn Ra < Rn/t

Req'd Rn = Ru/t < Rn Req'd Rn = Ra t < Rn

Ru / (tRn) < 1.00 Ra / (Rn/t) < 1.00

Which is: FORCE on a bolt < STRENGTH of a bolt

The STRENGTH of a bolt is computed by:

Simple Tension or Shear

Limit State

Specification Nominal Capacity

Typical Design

Variables

Tensile Rupture J3.6 Single Bolt Capacity:

FntAb

Bolt Material, Bolt Size

0.75 2.00

Shear Rupture J3.6 Single Shear Plane:

FnvAb


0.75 2.00

Slip Capacity J3.8 Single Shear Plane:

DuhscTb


0.75 2.00

Combined Shear and Tension:

Bearing Type Fasteners (-X or -N bolts):

Modify the nominal tensile rupture capacity for the presence of shear (SCM J3.7)

Apply the shear rupture limit state without modification

Limit State

Specification Nominal Capacity, Rn

Typical Design

Variables


F'ntAb


0.75 2.00

Shear Rupture J3.6 Single Shear Plane:

FnvAb


0.75 2.00

Slip Critical Type Fasteners (-SC bolts):

Modify the nominal slip capacity for the presence of tension (SCM J3.9)

Apply the tensile rupture limit state without modification

Limit State

Specification Nominal Capacity, Rn

Typical Design

Variables


FntAb


0.75 2.00

Slip Capacity J3.9 Single Shear Plane:

DuhscTbks


0.75 2.00

The FORCE on a bolt is computed by:

Forces Concentric with the Bolt Group at the Faying Surface:

All bolts are assumed to be equally stressed in tension. All shear planes are assumed to be equally stressed in shear.

Eccentricity in the Plane of the Faying Surface:

Elastic Vector Method: See SCM pg 7-8. Computes shear in the bolts. Direct method that is conservative and has an inconsistent factor of safety.

Instantaneous Center of Rotation Method: See SCM pg 7-6. Computes the relationship between the applied load and the shear load in the worst case bolt. Iterative method that is more consistent with test results and not as conservative as the Elastic Method.

Eccentricity out of the Plane of the Faying Surface:

Case I Method: See SCM pg 7-10. Basic mechanics (Mc/I) using the compression contact area to find the tension in the worst case bolt. Finding Ix may be iterative. If the shear is concentric with the bolt group it is equally divided among the shear planes otherwise use either the elastic vector or IC method to find the bolt shear forces.

Case II Method: See SCM pg 7-12. Uses basic statics (Applied Moment = Pe = rat n' dm= Internal Moment) without considering the contact area to find the tension in the worst case bolt. If the shear is concentric with the bolt group it is equally divided among the shear planes otherwise use either the elastic vector or IC method to find the bolt shear forces.

http://www.bgstructuralengineering.com/BGSCM/BGSCM004/BGSCM00403.htm#ICMethod

http://www.bgstructuralengineering.com/BGSCM/BGSCM004/BGSCM00403.htm#ElasticVector

http://www.bgstructuralengineering.com/BGSCM/BGSCM004/BGSCM00403.htm#ConcShear

http://www.bgstructuralengineering.com/BGSCM/BGSCM004/BGSCM00403.htm#ConcTens

lrfd design spreadsheet

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