Anchor Bolt Design Calculator

Anchor Bolt Interaction & Capacity Calculator

1. Input Parameters

Factored Tension Force, $T$ (kN):

Factored Shear Force, $V$ (kN):

Factored Overturning Moment, $M$ (kN·m):

Total Number of Bolts ($n$):

Number of Bolt Rows in Moment Axis ($n_y$):

Distance of Outer Bolt Row from Centroid, $y$ (mm):

2. Bolt Capacities (Governing Limits)

Allowable Tensile Capacity, $T_{all}$ (kN):

Allowable Shear Capacity, $V_{all}$ (kN):

Calculation Summary

Max Single Bolt Tensile Force ($T_i$): - kN

Single Bolt Shear Force ($V_{bolt}$): - kN

Interaction Ratio: $\left(\frac{T_u}{T_{all}}\right)^2 + \left(\frac{V_u}{V_{all}}\right)^2 = $ -

Design Status: Pending

Worked Example

Problem: A baseplate configuration uses 4 anchor bolts arranged symmetrically ($2 \times 2$ grid). The outer row is located $150\text{ mm}$ from the centroid. The connection is subjected to $T = 40\text{ kN}$, $V = 25\text{ kN}$, and $M = 12\text{ kN}\cdot\text{m}$. Factored tensile capacity $T_{all} = 45\text{ kN}$ and shear capacity $V_{all} = 30\text{ kN}$.

Solution:

• Direct Tension per bolt: $T / n = 40 / 4 = 10\text{ kN}$
• Moment-induced Tension: $\sum y_j^2 = 2 \times (150)^2 + 2 \times (-150)^2 = 90,000\text{ mm}^2$.
  $T_M = \frac{12 \times 10^6 \times 150}{90,000} = 20,000\text{ N} = 20\text{ kN}$.
• Total Peak Tensile Load ($T_i$): $10\text{ kN} + 20\text{ kN} = 30\text{ kN}$.
• Shear per bolt ($V_{bolt}$): $25 / 4 = 6.25\text{ kN}$.
• Interaction Equation Check: $$\left(\frac{30}{45}\right)^2 + \left(\frac{6.25}{30}\right)^2 = (0.667)^2 + (0.208)^2 = 0.445 + 0.043 = 0.488 \le 1.0 \quad \mathbf{[SAFE]}$$

Anchor Bolt Design Theory & Principles

Anchor bolts connect structural steel column base plates to concrete foundations, transferring tensile force ($T$), shear force ($V$), and bending moments ($M$).

1. Tension Calculation

The total tensile demand on the most critical bolt includes direct axial tension and tension due to the overturning moment:

$$T_i = \frac{T}{n} + \frac{M \cdot y_i}{\sum (y_j^2)}$$

Where:

• $n$ = Total number of anchor bolts.
• $y_i$ = Distance from the centroid to the extreme tension bolt row.
• $\sum (y_j^2)$ = Sum of squared distances of all bolts relative to the neutral axis of the group.

2. Shear Distribution

Assuming a rigid base plate, shear force is distributed uniformly across all bolts:

$$V_{\text{bolt}} = \frac{V}{n}$$

3. Combined Tension & Shear Interaction Formula

According to standard design codes (such as IS 800, ACI 318, and Eurocode 2 - Part 4), combined tension and shear loads must satisfy the elliptical interaction check:

$$\left(\frac{T_u}{T_{\text{all}}}\right)^2 + \left(\frac{V_u}{V_{\text{all}}}\right)^2 \le 1.0$$

4. Critical Failure Modes

Force Type	Steel Failure Modes	Concrete Failure Modes
Tension	Anchor rod yield/ductile rupture	Concrete cone breakout, Pull-out (bond) failure, Splitting failure
Shear	Anchor rod shear failure	Concrete edge breakout, Concrete pry-out failure

5. Standard Spacing & Detailing Rules

• Minimum Edge Distance: $\ge 1.5 \, d_b$ (where $d_b$ is nominal bolt diameter).
• Minimum Spacing: $\ge 2.0 \, d_b$.
• Grouting: Ensure proper leveling grout beneath base plate prior to final torque.