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Analyze bolted connections under eccentric and combined loading conditions
Applied Load (P): kN
Eccentricity (e): mm
Bolt Diameter (d): mm
Direction:
Critical Bolt X: mm
Critical Bolt Y: mm
n = ∑(num_bolts)
n = bolts
∑(x² * n) = Sum of all (distance² * num_bolts)
∑(x² * n) = mm²
∑(y² * n) = Sum of all (distance² * num_bolts)
∑(y² * n) = mm²
J = ∑(x² * n) + ∑(y² * n)
J = +
J = mm⁴
T = P * e
T = *
T = kN-mm
Rdx = P / n (load to the right)
Rdx = /
Rdx = kN
Rdy = 0 (no vertical component)
Rdy = P / n (load downward)
Rdy = /
Rdy = kN
Rdx = 0 (no horizontal component)
Rtx = (T * ycrit) / J
Rtx = ( * ) /
Rtx = kN
Rty = (T * xcrit) / J
Rty = ( * ) /
Rty = kN
Rt = √[(Rtx)² + (Rty)²]
Rt = √[()² + ()²]
Rt = kN
Rx = Rdx + Rtx
Rx = +
Rx = kN
Ry = Rdy + Rty
Ry = +
Ry = kN
Abolt = (π/4) * d²
Abolt = (π/4) * ()²
Abolt = mm²
Rmax = √[(Rx)² + (Ry)²]
Rmax = √[()² + ()²]
Rmax = kN
fvmax = (Rmax / Abolt) * 1000
fvmax = ( / ) * 1000
fvmax = MPa
Number of Bolts (n):
Applied Load (Tload): kN
Angle (θ): º
Fastener Type:
Threads:
Connection Type:
Max Pretension (Tb): kN
Allowable Shear (Fvall): MPa
Ultimate Tensile (Fu): MPa
Ab = (π/4) × d²
Ab = (π/4) × ()²
Ab = mm²
Th = Tload × cos(θ)
Th = × cos(º)
Th = kN
Tv = Tload × sin(θ)
Tv = × sin(º)
Tv = kN
ft = (Tv / (n × Ab)) × 1000
ft = ( / ( × )) × 1000
ft = MPa
fv = (Th / (n × Ab)) × 1000
fv = ( / ( × )) × 1000
fv = MPa
Ft = 0.33 × Tb / Ab × 1000 (Slip-Critical)
Ft = 0.33 × / × 1000
Ft determined from NSCP Table (Bearing-type)
Ft = MPa
F'v = Fvall × (1 - ft / Ft)
F'v = × (1 - / )
F'v = Fv × (1 - ft / (1.2 × Ft))
F'v calculated from NSCP bearing-type formula
F'v = MPa
Check 1: ft ≤ Ft
MPa ≤ MPa
Check 2: fv ≤ F'v
Direct loads per bolt: Rdx = Px/n, Rdy = Py/n
Formula: T = (Px * y) + (Py * x)
Specify the direction of each force component based on your bolt location and loading diagram.
Rmax = √(Rx² + Ry²)
fvmax = Rmax / Abolt
Px = kN
Py = kN
d = mm
Rdx = Px / n
Rdx = / = kN
Rdy = Py / n
Rdy = / = kN
∑(n)(x)²
Sum of X-coordinates = mm²
∑(n)(y)²
Sum of Y-coordinates = mm²
J = ∑(n)(x)² + ∑(n)(y)²
J = + = mm²
T = (Px * y) + (Py * x)
T = ( * ) + ( * )
Rtx = (T * y_bolt) / J
Rty = (T * x_bolt) / J
Rt = √(Rtx² + Rty²)
Rt = √(()² + ()²)
Rx = Rdx () Rtx ()
Rx =
Ry = Rdy () Rty ()
Ry =
Rmax = √(()² + ()²)
A_bolt = (π/4) * d²
A_bolt = (π/4) * ()²
A_bolt = mm²
fvmax = (Rmax / A_bolt) * 1000
Given:
• fvmax = MPa
• Rmax = kN
Convert Rmax from kN to N:
Rmax = kN × 1000 = N
We know that:
Where:
Abolt = (π/4) × d²
Abolt = Rmax / fvmax
(π/4) × d² = Rmax / fvmax
d² = (4 × Rmax) / (π × fvmax)
d = √[(4 × Rmax) / (π × fvmax)]
Using π = 3.14159 and Rmax in N:
d = √[(4 × ) / (3.14159 × )]
d = √[ / ]
• Fu = MPa
• d = mm
• n = bolts
• Rmax = kN = N
For bearing stress connection:
Rmax(N) = 1.2 × Fu(MPa) × d(mm) × t(mm) × n
Note: Rmax must be in Newton (N) for this formula. 1 kN = 1000 N
t(mm) = Rmax(N) / (1.2 × Fu × d × n)
t = N / (1.2 × MPa × mm × )
t = /
t = mm
Fill these fields if you want to check tensile stress due to eccentricity
Shear: | Tensile:
Shear:
• Given Load = kN
• Number of bolts (n) =
• Diameter (d) = mm
• Fastener Type =
• Threads =
• Connection Type = Bearing-type
• Ultimate Tensile (Fu) = MPa
Abolt = (π/4) × ²
fv = Load / (Abolt × n)
fv = ( × 1000) / ( × )
Based on with threads (NSCP Table - Bearing-type):
Fv = MPa
M = Load × e
M = ×
M = kN·mm
ft = (M × y) / (Abolt × Σy²)
ft = ( × 1000 × ) / ( × )
Based on bearing-type formula:
Condition for T (Tensile Stress):
ft = P
Condition for fv (Shear Stress):
fv = P
Assume Ft = ft (Interaction Limit):
- (fv) = ft
- ( P) = P
√(² - fv²) = ft
Safe Value of P = kN
(Controlled by: )
Case A: Use when you have direct horizontal and vertical load components Case B: Use when you have eccentric load with bolt group configuration
Example: Th = 0.894427P (horizontal load component in terms of P)
Example: Tv = 0.447214P (vertical load component in terms of P)
Distance from center of gravity to load application point
Distance from center of gravity to critical bolt
Enter the Y-coordinates for the bolt group. Include all unique Y distances from the center of gravity.
Critical bolt area for tension
= π/4 × d²
= ×
Horizontal component (N)
Vertical component (N)
Bolt group moment of inertia term
T = CT × P (tension in N)
Number of Bolts/Rivets (n):
Nominal Area (One Bolt) Ab: (π/4) × ² = mm²
BEARING-TYPE CONNECTION - CASE A:
Equation for Th: (Horizontal Load Component)
Equation for Tv: (Vertical Load Component)
BEARING-TYPE CONNECTION - CASE B (ECCENTRIC LOADING):
Distance to Farthest Bolt (y): mm
∑y²n (Bolt Group): mm²
Bolt Group Y-Coordinates:
• y = mm, n = bolts
Case Type:
From "":
CTh = → Th = × P (N)
CTv = → Tv = × P (N)
Calculate Stresses:
• ft = Th / (Ab × n) = ( × P) / ( × ) = × P (MPa)
• fv = Tv / (Ab × n) = ( × P) / ( × ) = × P (MPa)
Calculate Tension Force:
• T = P(e)(y) / ∑y²
• T = P()() /
• T = × P (N)
• ft = T / Ab = ( × P) / = × P (MPa)
• fv = P / (Ab × n) = P / ( × ) = × P (MPa)
NSCP Table Formula (Bearing-Type):
Assumption: ft = Ft (Actual tensile stress equals allowable tensile stress)
Solution Steps:
Psafe = kN ( N)
