ANCHOR BOLT CALCULATION

Anchor bolts are essential components in construction, providing a reliable connection between structural and non-structural elements. They transfer loads from the attached element to the concrete substrate, ensuring stability and preventing movement. Understanding the principles behind anchor bolt calculation is crucial for engineers and construction professionals to guarantee the safety and longevity of structures.

Types of Anchor Bolts

Anchor bolts come in various types, each designed for specific applications and load conditions. Some common types include:

• Cast-in-place anchor bolts: These are embedded in the concrete during the pouring process. They typically consist of a threaded rod with a bent or headed end to provide mechanical interlock with the concrete.
• Post-installed mechanical anchors: These are installed in hardened concrete after it has cured. They rely on mechanical interlock or friction to resist pullout forces. Examples include expansion anchors, undercut anchors, and screw anchors.
• Bonded anchors: These anchors use adhesive to bond the anchor to the concrete. They offer high strength and are suitable for applications where mechanical anchors may not be feasible.

Factors Affecting Anchor Bolt Capacity

The capacity of an anchor bolt depends on several factors, including:

• Concrete strength: Higher concrete strength generally leads to higher anchor bolt capacity.
• Anchor bolt size and material: Larger diameter bolts and higher strength materials can withstand greater loads.
• Embedment depth: Deeper embedment provides greater resistance to pullout forces.
• Edge distance: The distance from the anchor bolt to the edge of the concrete member affects its capacity. Closer edge distances reduce the capacity.
• Anchor spacing: The spacing between anchor bolts influences the load distribution and overall capacity of the connection.
• Loading conditions: The type of load (tension, shear, or combined) and its magnitude affect the anchor bolt's performance.

Anchor Bolt Calculation Methods

Several methods are available for calculating anchor bolt capacity, including:

• American Concrete Institute (ACI) 318: This is a widely used standard that provides detailed guidelines for anchor bolt design. It considers various failure modes, such as concrete breakout, steel yielding, and pullout.
• European Technical Assessment (ETA): This is a European standard that provides guidelines for the assessment and approval of anchor bolts.
• Finite element analysis (FEA): This is a numerical method that can be used to analyze the behavior of anchor bolts under complex loading conditions.

ACI 318 Approach to Anchor Bolt Calculation

The ACI 318 standard provides a comprehensive approach to anchor bolt design, considering various failure modes and safety factors. The following steps outline the general procedure for calculating anchor bolt capacity according to ACI 318:

1. Determine the factored loads: Calculate the factored tension and shear loads acting on the anchor bolt, considering appropriate load combinations.
2. Determine the anchor bolt type and size: Select an appropriate anchor bolt type and size based on the application and load requirements.
3. Determine the concrete strength: Obtain the specified compressive strength of the concrete.
4. Calculate the concrete breakout strength in tension: This is the resistance of the concrete to a cone-shaped failure around the anchor bolt. The ACI 318 standard provides equations for calculating the concrete breakout strength based on the anchor bolt size, embedment depth, edge distance, and concrete strength.
5. Calculate the concrete breakout strength in shear: This is the resistance of the concrete to a shear failure along a plane extending from the anchor bolt to the edge of the concrete member. The ACI 318 standard provides equations for calculating the concrete breakout strength in shear based on the anchor bolt size, edge distance, and concrete strength.
6. Calculate the steel strength in tension: This is the tensile capacity of the anchor bolt itself. The ACI 318 standard provides equations for calculating the steel strength based on the anchor bolt's yield strength and cross-sectional area.
7. Calculate the steel strength in shear: This is the shear capacity of the anchor bolt itself. The ACI 318 standard provides equations for calculating the steel strength based on the anchor bolt's yield strength and cross-sectional area.
8. Calculate the pullout strength: This is the resistance of the anchor bolt to being pulled out of the concrete. The ACI 318 standard provides equations for calculating the pullout strength based on the anchor bolt type, embedment depth, and concrete strength.
9. Calculate the side-face blowout strength: This failure mode is relevant for headed anchors near an edge. The ACI 318 standard provides equations for calculating the side-face blowout strength.
10. Determine the controlling failure mode: The controlling failure mode is the one with the lowest capacity. This is the failure mode that will govern the design.
11. Apply safety factors: Apply appropriate safety factors to the calculated capacities to account for uncertainties in the design parameters and to ensure a safe design. The ACI 318 standard specifies the required safety factors for different failure modes.
12. Verify the design: Ensure that the factored loads are less than or equal to the design strength (capacity divided by the safety factor) for all failure modes.

Detailed Explanation of Key Calculations

Let's delve deeper into some of the key calculations involved in anchor bolt design according to ACI 318.

Concrete Breakout Strength in Tension (N_cb)

The concrete breakout strength in tension represents the resistance of the concrete to a cone-shaped failure emanating from the anchor. The ACI 318 equation for calculating N_cb is:

N_cb = A_nc / A_nco ψ_ed,N ψ_c,N ψ_cp,N N_b

Where:

• A_nc is the projected concrete failure area for the anchor or group of anchors.
• A_nco is the projected concrete failure area for a single anchor, not limited by edge distance or spacing.
• ψ_ed,N is a modification factor for edge distance effects.
• ψ_c,N is a modification factor for cracking effects.
• ψ_cp,N is a modification factor for post-installed anchors designed for uncracked concrete.
• N_b is the basic concrete breakout strength of a single anchor in tension.

The terms A_nc and A_nco account for the influence of anchor spacing and edge distances on the failure area. The ψ factors adjust the breakout strength based on the presence of cracks, edge proximity, and whether the anchor is designed for cracked or uncracked concrete. The basic concrete breakout strength, N_b, is calculated as:

N_b = k_c λ_a √(f'_c) h_ef^1.5

Where:

• k_c is a coefficient that depends on the anchor type (e.g., 17 for cast-in anchors, 14 for post-installed anchors).
• λ_a is a modification factor for lightweight concrete.
• f'_c is the specified compressive strength of the concrete.
• h_ef is the effective embedment depth of the anchor.

Concrete Breakout Strength in Shear (V_cb)

The concrete breakout strength in shear represents the resistance of the concrete to a shear failure along a plane extending from the anchor to the edge of the concrete member. The ACI 318 equation for calculating V_cb is:

V_cb = A_vc / A_vco ψ_ed,V ψ_c,V ψ_h,V V_b

Where:

• A_vc is the projected concrete failure area for the anchor or group of anchors.
• A_vco is the projected concrete failure area for a single anchor, not limited by edge distance or spacing.
• ψ_ed,V is a modification factor for edge distance effects.
• ψ_c,V is a modification factor for cracking effects.
• ψ_h,V is a modification factor for anchors located in high-humidity environments.
• V_b is the basic concrete breakout strength of a single anchor in shear.

Similar to the tension breakout calculation, the terms A_vc and A_vco account for the influence of anchor spacing and edge distances. The ψ factors adjust the breakout strength based on the presence of cracks, edge proximity, and humidity. The basic concrete breakout strength, V_b, is calculated as:

V_b = 0.7 √(d_a) λ_a √(f'_c) l_e^0.2 h_ef

Where:

• d_a is the diameter of the anchor.
• λ_a is a modification factor for lightweight concrete.
• f'_c is the specified compressive strength of the concrete.
• l_e is the length of the anchor in shear.
• h_ef is the effective embedment depth of the anchor.

Steel Strength in Tension (N_sa) and Shear (V_sa)

The steel strength in tension and shear represents the capacity of the anchor bolt itself to resist tensile and shear forces. These values are determined based on the anchor bolt's material properties and cross-sectional area.

The steel strength in tension is calculated as:

N_sa = A_se,N f_uta

Where:

• A_se,N is the effective cross-sectional area of the anchor in tension.
• f_uta is the specified tensile strength of the anchor material.

The steel strength in shear is calculated as:

V_sa = 0.6 A_se,V f_uta

Where:

• A_se,V is the effective cross-sectional area of the anchor in shear.
• f_uta is the specified tensile strength of the anchor material.

Pullout Strength (N_p)

The pullout strength represents the resistance of the anchor to being pulled out of the concrete. This failure mode is particularly relevant for headed anchors and undercut anchors. The ACI 318 standard provides equations for calculating the pullout strength based on the anchor type, embedment depth, and concrete strength. The specific equation varies depending on the anchor type.

Side-Face Blowout Strength

Side-face blowout is a potential failure mode for headed anchors located near an edge. It involves the concrete cracking and spalling along the side face of the concrete member. The ACI 318 standard provides equations for calculating the side-face blowout strength, which depend on the anchor size, edge distance, and concrete strength.

Importance of Proper Installation

Even with accurate calculations, the actual performance of anchor bolts depends heavily on proper installation. Incorrect installation can significantly reduce the anchor's capacity and lead to premature failure. Some key aspects of proper installation include:

• Drilling the correct hole size and depth: Using the wrong drill bit or drilling to the wrong depth can compromise the anchor's embedment and load transfer.
• Cleaning the hole: Dust and debris in the hole can prevent proper bonding between the anchor and the concrete.
• Using the correct torque: Over-torquing or under-torquing the anchor can damage the anchor or the concrete.
• Following the manufacturer's instructions: Always follow the manufacturer's instructions for installation, as they provide specific guidance for each anchor type.

Software and Tools for Anchor Bolt Calculation

Several software programs and online tools are available to assist engineers in performing anchor bolt calculations. These tools can automate the calculations, check for errors, and generate reports. Some popular software programs include:

• Hilti PROFIS Engineering: This software provides comprehensive anchor design capabilities, including calculations according to ACI 318 and other standards.
• Simpson Strong-Tie Anchor Designer: This software allows engineers to design anchor connections using Simpson Strong-Tie anchors.
• Powers Fasteners Anchor Design Software: This software provides anchor design capabilities for Powers Fasteners anchors.

Conclusion

Anchor bolt calculation is a critical aspect of structural design, ensuring the safe and reliable connection of structural and non-structural elements to concrete. Understanding the principles behind anchor bolt design, including the various failure modes and the factors that affect anchor capacity, is essential for engineers and construction professionals. The ACI 318 standard provides a comprehensive framework for anchor bolt design, considering various failure modes and safety factors. By following the guidelines outlined in ACI 318 and ensuring proper installation, engineers can design anchor bolt connections that meet the required performance criteria and contribute to the overall safety and longevity of structures. Remember to always consult with a qualified engineer for complex or critical anchor bolt designs.

Table of Anchor Bolt Types and Applications

Disclaimer: This article provides general information about anchor bolt calculation and should not be considered a substitute for professional engineering advice. Always consult with a qualified engineer for specific design recommendations.