Prying Action in Bolted Tension Connections — AISC 360 & EN 1993 Design Guide

When a bolted tension connection is loaded, the bolts do not simply carry the applied force. The connected flange or angle leg bends, levers against the bolt line, and generates an additional force in the bolts that can far exceed the external load. This is prying action — and ignoring it is one of the most common and dangerous mistakes in connection design.

In this guide: We cover the mechanics of prying action, the T-stub flange model used by AISC 360 Part 9 and EN 1993-1-8 Clause 6.2.4, the prying force Q calculation, flange thickness requirements to eliminate prying, a complete worked example for an angle tension connection, and a sensitivity analysis showing how prying force varies with flange thickness. Verify every calculation with our free bolted connections calculator.

PRELIMINARY — NOT FOR CONSTRUCTION. All results discussed are for educational and reference use only. Must be independently verified by a licensed Professional Engineer or Structural Engineer before use in any project.

What Is Prying Action and Why It Matters

Consider a T-stub connection — a T-section with its flange bolted to a supporting member and its stem welded to a beam or brace. When a tensile force P is applied to the stem, the bolts resist it in direct tension. However, the flange between the bolt line and the stem bends upward, while the flange tip beyond the bolt line presses downward against the supporting surface. This creates a lever mechanism: the bolt acts as a fulcrum, the applied tension P pulls up on one side, and the flange tip bearing against the support pushes down on the other.

The result is an additional force Q (the prying force) in each bolt, which can increase the bolt tension demand by 30% to 60% — and in extreme cases with thin flanges, by over 100%. A connection designed with only direct tension in mind may have bolts that appear to have adequate capacity but fail prematurely when prying is included.

The three physical consequences of prying action are:

1. Higher bolt tension demand — each bolt sees P (direct tension) + Q (prying), not just P.
2. Flange bending stress — the flange itself must be thick enough to resist the bending moment between the bolt line and the stem face.
3. Flange tip bearing — the flange tips bear against the support, generating localized compressive stresses that may crush the support surface.

The T-Stub Flange Model

The T-stub is the canonical model for prying analysis. Whether you are designing a bolted moment end plate, a tee hanger, a split-tee brace connection, or a bolted angle in tension, the T-stub analogy applies. The model assumes:

• The flange behaves as a simple beam in bending, with plastic hinges forming at the bolt centerline and at the stem face (or web line).
• The bolt provides a concentrated reaction at its centerline.
• The prying force Q acts at the flange tip, where the flange bears against the supporting surface.

Geometry and Notation (AISC 360 Part 9 Convention)

           a     a'      b'       b
    |<--------->|<--->|<------>|<----->
    |                                     |
    |    Q                              |     Q
    |    |                              |     |
    |    v                              |     v
    ======        BOLT         BOLT        ======
    |     |         O            O         |     |
    |     |         |            |         |     |
    |     ================================     |  <-- flange
    |               |            |               |
    |               |            |               |
    |               ==============               |
    |                    | |                     |
    |                    | | Stem (web)          |
    |                    | |                     |
    |                  P/2 P/2                   |

Key dimensions:

The critical geometric ratio for prying is b'/a'. When b'/a' is large (i.e., the bolt is far from the flange tip relative to its distance from the stem), prying is amplified because the lever ratio favors moment transfer to the bolt.

Prying Force Q — AISC 360 Part 9 Approach

The AISC Manual Part 9 provides a direct calculation for the prying force per bolt. The approach assumes the flange reaches its plastic moment capacity at the bolt line and the stem face, and that the bolt force is the sum of the direct tension component plus the prying contribution.

Step 1: Determine the required tension per bolt (direct):

$$T_{req} = \frac{P_u}{n_b}$$

Where $P_u$ is the factored applied tension and $n_b$ is the number of bolts.

Step 2: Check whether the flange thickness is adequate to eliminate prying:

$$t_{min} = \sqrt{\frac{4 \cdot T_u \cdot b'}{\phi \cdot p \cdot F_y}}$$

Where:

• $T_u$ = nominal tensile strength of one bolt ($F_{nt} \cdot A_b$)
• $b'$ = distance from bolt centerline to plastic hinge at stem face
• $p$ = tributary length per bolt (bolt spacing or effective width)
• $F_y$ = flange yield strength
• $\phi = 0.90$ (LRFD)

If the actual flange thickness $t_f \geq t_{min}$, prying can be neglected — the flange is stiff enough that prying forces do not develop.

Step 3: If prying cannot be neglected, calculate the prying force Q:

The required flange flexural strength parameter:

$$\alpha = \frac{1}{\delta} \cdot \left[ \frac{4 \cdot T_{req} \cdot b'}{\phi \cdot p \cdot t_f^2 \cdot F_y} - 1 \right]$$

Where $\delta = 1 - d'/p$ is the net area ratio (accounting for the bolt hole), and $d'$ is the bolt hole diameter.

The prying force per bolt is then:

$$Q = \frac{b'}{a'} \cdot \left[ \alpha \cdot \delta \cdot \frac{\phi \cdot p \cdot t_f^2 \cdot F_y}{4 \cdot b'} - \frac{P_u}{2} \right]$$

In practice, AISC provides a simplified tabular procedure in Part 9 (Tables 9-2 through 9-8) that precomputes the available tensile strength including prying effects for common tee geometries.

Final bolt tension demand including prying:

$$T_{total} = T_{req} + Q$$

Check:

$$T_{total} \leq \phi \cdot T_u = \phi \cdot F_{nt} \cdot A_b$$

Where $\phi = 0.75$ for bolts in tension.

EN 1993-1-8 T-Stub Model (Component Method)

The Eurocode takes a component-based approach through three distinct failure modes, treating the T-stub flange as equivalent to a simple beam with two potential plastic hinges.

Equivalent T-Stub in Tension — EN 1993-1-8 Clause 6.2.4

The T-stub model in the Eurocode is the basis for all bolted tension zone calculations, including column flange in bending, end plate in bending, and angle cleats in tension. The model identifies three failure modes that together capture the full range of prying behavior.

Mode 1 — Complete Flange Yielding (No Bolt Failure)

The flange is thin relative to the bolt strength. Two plastic hinges form (one at the stem face, one at the bolt line), and the flange yields completely. Prying forces are at their maximum. The design resistance is:

$$F_{T,1,Rd} = \frac{4 \cdot M_{pl,1,Rd}}{m}$$

Where:

• $M_{pl,1,Rd} = 0.25 \cdot \sum l_{eff,1} \cdot t_f^2 \cdot f_y / \gamma_{M0}$
• $m$ = distance from bolt centerline to plastic hinge at stem face (equivalent to AISC's b')
• $\sum l_{eff,1}$ = sum of effective lengths for Mode 1 (circular or non-circular yield line patterns)
• $\gamma_{M0} = 1.00$ (recommended)

Mode 1 is the prying-dominant mode. The bolt strength does not appear in the equation — the connection fails because the flange yields, regardless of bolt capacity.

Mode 2 — Combined Flange Yielding + Bolt Failure

The flange is of intermediate thickness. One plastic hinge forms at the stem face, and the bolts also reach their ultimate capacity. The design resistance is:

$$F_{T,2,Rd} = \frac{2 \cdot M_{pl,2,Rd} + n \cdot \sum F_{t,Rd}}{m + n}$$

Where:

• $M_{pl,2,Rd} = 0.25 \cdot \sum l_{eff,2} \cdot t_f^2 \cdot f_y / \gamma_{M0}$
• $n = \min(e_{min}, 1.25 \cdot m)$ — effective distance to the prying force
• $\sum F_{t,Rd}$ = sum of bolt tension resistances
• $F_{t,Rd} = 0.9 \cdot f_{ub} \cdot A_s / \gamma_{M2}$ per bolt

Mode 2 is a transition mode — some prying develops, but the bolts contribute meaningfully to the resistance.

Mode 3 — Bolt Failure Only (No Prying)

The flange is thick enough to remain essentially rigid. Two plastic hinges form at the bolt line, and the connection fails by bolt tension alone. Prying forces are zero in this mode. The design resistance is:

$$F_{T,3,Rd} = \sum F_{t,Rd}$$

Where $\sum F_{t,Rd}$ is simply the sum of all bolt tension resistances.

The controlling failure mode is the minimum of Modes 1, 2, and 3: $$F_{T,Rd} = \min(F_{T,1,Rd}, F_{T,2,Rd}, F_{T,3,Rd})$$

Effective Lengths ($l_{eff}$)

The effective length represents the tributary width of flange participating in yielding. The Eurocode provides two patterns:

• Circular yield line pattern ($l_{eff,cp}$): individual circular yield mechanisms around each bolt — relevant for large bolt spacings.
• Non-circular yield line pattern ($l_{eff,nc}$): continuous yield lines across the full bolt group — relevant for closely spaced bolts.

For a single bolt row, typical values are:

• $l_{eff,cp} = 2 \cdot \pi \cdot m$
• $l_{eff,nc} = 4 \cdot m + 1.25 \cdot e$ (where e is the edge distance)

The designer takes the minimum of circular and non-circular effective lengths for Mode 1, and the non-circular length for Mode 2.

Worked Example — Bolted Angle in Tension with Prying Check

Problem Statement

A pair of L4x4x1/2 angles (Grade A36, $F_y = 36$ ksi, $F_u = 58$ ksi) is bolted to a gusset plate with two rows of 3/4-inch diameter A325-N bolts (one row per angle leg). The applied factored tension is $P_u = 80$ kips. Determine whether prying action governs the bolt design.

Geometry:

Step 1: Direct Tension Demand

$$T_{req} = \frac{P_u}{n_b} = \frac{80}{6} = 13.33\text{ kips/bolt}$$

Step 2: Compute Prying Geometry per AISC 360 Part 9

The distance from bolt centerline to the plastic hinge at the stem face (the angle heel, where the outstanding leg meets the attached leg):

$$b = g - k = 2.50 - 1.125 = 1.375\text{ in}$$

where $k = 1.125$ in for L4x4x1/2 (distance from heel to face of attached leg).

$$b' = b - \frac{d_b}{2} = 1.375 - 0.375 = 1.000\text{ in}$$

The distance from bolt centerline to the plastic hinge at the flange tip:

$$a = 1.50\text{ in (edge distance)}$$

$$a' = a + \frac{d_b}{2} = 1.50 + 0.375 = 1.875\text{ in}$$

Lever ratio:

$$\frac{b'}{a'} = \frac{1.000}{1.875} = 0.533$$

The lever ratio of 0.533 means the prying force Q will be approximately 53% of the force transferred through the flange bending mechanism — a significant contribution.

Tributary length per bolt:

$$p = 3.00\text{ in}$$

Net area ratio:

$$\delta = 1 - \frac{d_h}{p} = 1 - \frac{0.8125}{3.00} = 0.729$$

Step 3: Flange Thickness Required to Eliminate Prying

The bolt nominal tensile strength:

$$T_u = F_{nt} \cdot A_b = 90 \times 0.442 = 39.78\text{ kips}$$

The required flange thickness to prevent prying (AISC 360 Part 9 Eq. 9-28):

$$t_{min} = \sqrt{\frac{4 \cdot T_u \cdot b'}{\phi \cdot p \cdot F_y}} = \sqrt{\frac{4 \times 39.78 \times 1.000}{0.90 \times 3.00 \times 36}}$$

$$t_{min} = \sqrt{\frac{159.12}{97.2}} = \sqrt{1.637} = 1.279\text{ in}$$

The actual angle leg thickness is $t_f = 0.50$ in, which is significantly less than $t_{min}$ (1.279 in). Therefore, prying cannot be neglected — the angle leg is far too thin to resist the bolt tension without deforming.

Step 4: Calculate Prying Force Q

Using the AISC method with the calculated parameters:

Flange moment capacity parameter:

The required moment at the bolt line per unit width:

Determine $\alpha$ from the prying equilibrium equation. For a flange with $t_f < t_{min}$, we solve for the maximum prying force that the flange can develop before yielding:

The available flange flexural strength per unit width:

$$M_p = \phi \cdot \frac{p \cdot t_f^2 \cdot F_y}{4} = 0.90 \times \frac{3.00 \times 0.50^2 \times 36}{4} = 0.90 \times \frac{27.0}{4} = 6.075\text{ kip-in}$$

The required moment at the bolt line from direct tension:

$$M_{req} = T_{req} \cdot b' = 13.33 \times 1.000 = 13.33\text{ kip-in}$$

Since $M_{req} > M_p$ (13.33 > 6.075), the direct tension alone exceeds the flange moment capacity. The prying analysis confirms the flange is inadequate.

Compute the maximum bolt tension the flange can support:

$$\alpha_{max} = \frac{M_p}{M_{req}} \cdot \frac{1}{\delta} = \frac{6.075}{13.33} \times \frac{1}{0.729} = 0.456 \times 1.372 = 0.625$$

This $\alpha < 1.0$ confirms prying is active. The prying force Q per bolt is:

The flange moment equilibrium requires:

$$T_{req} \cdot b' - M_p + Q \cdot a' = 0$$

$$Q = \frac{M_p - T_{req} \cdot b'}{a'} = \frac{6.075 - 13.33}{1.875} = \frac{-7.255}{1.875} = -3.87\text{ kips}$$

The negative value indicates that even without prying, the flange cannot resist the direct tension. The connection must be redesigned.

Total bolt tension demand:

With the current geometry, the tension demand (13.33 kips) exceeds what the flange can transfer without yielding. The bolts themselves have adequate pure tension capacity ($\phi T_u = 0.75 \times 39.78 = 29.84$ kips), but the thin angle leg fails the prying check.

Step 5: Redesign Options

Three options exist to resolve the prying issue:

Option 1 — try L4x4x3/4 ($t_f = 0.75$ in, $k = 1.25$ in):

Updated geometry:

• $b = 2.50 - 1.25 = 1.25$ in
• $b' = 1.25 - 0.375 = 0.875$ in
• $a' = 1.50 + 0.375 = 1.875$ in

Updated $t_{min}$:

$$t_{min} = \sqrt{\frac{4 \times 39.78 \times 0.875}{0.90 \times 3.00 \times 36}} = \sqrt{\frac{139.23}{97.2}} = \sqrt{1.432} = 1.197\text{ in}$$

$t_f = 0.75$ in < $t_{min} = 1.197$ in — prying is still not eliminated.

Updated flange moment capacity:

$$M_p = 0.90 \times \frac{3.00 \times 0.75^2 \times 36}{4} = 0.90 \times \frac{60.75}{4} = 13.67\text{ kip-in}$$

Updated required moment:

$$M_{req} = 13.33 \times 0.875 = 11.66\text{ kip-in}$$

Now $M_p = 13.67 > M_{req} = 11.66$ — the flange has sufficient moment capacity. The prying force Q:

$$Q = \frac{13.67 - 11.66}{1.875} = 1.07\text{ kips}$$

Total bolt tension: $T_{total} = 13.33 + 1.07 = 14.40$ kips.

Bolt capacity check: $\phi T_u = 0.75 \times 39.78 = 29.84$ kips > 14.40 kips. OK.

D/C ratio = 14.40 / 29.84 = 0.483. The 3/4-inch bolt is still adequate with the thicker angle.

Worked Example Summary

The prying force Q of 1.07 kips represents an 8% increase over the direct tension demand. While modest here, this demonstrates that even when the flange "passes," prying still creates additional bolt demand that must be checked.

AISC 360 vs EN 1993-1-8 — Prying Design Comparison

Both codes use the same fundamental T-stub mechanics, but the design approach differs significantly in execution.

The key practical difference: AISC gives you an explicit yes/no prying criterion ($t_{min}$) and a direct Q value. Eurocode requires you to compute all three failure modes and observe which governs. If Mode 3 governs, prying is zero. If Mode 1 or 2 govern, prying is present and the resistance formula accounts for it.

When the Codes Agree and When They Diverge

For thick flanges ($t_f$ well above the prying-elimination threshold), both codes converge: bolt tension governs, and no prying reduction applies. The difference is in the partial factor — AISC uses $\phi = 0.75$, Eurocode uses $1/\gamma_{M2} = 0.80$.

For thin flanges, the Eurocode Mode 1 generally yields a lower resistance than the AISC approach because Mode 1 assumes zero bolt contribution — the flange alone determines the capacity. The AISC approach allows some bolt-flange interaction even for thin flanges, albeit with high prying forces.

Sensitivity Analysis — Prying Force vs Flange Thickness

Using the worked example geometry (L4x4 angle, 3/4 in A325 bolts, b' = 1.00 in, a' = 1.875 in, p = 3.00 in), the prying force Q varies dramatically with flange thickness:

Key observations from the sensitivity analysis:

• At $t_f = 0.625$ in, prying adds 36% to the bolt tension demand. This is the classic prying regime — the flange bends enough to generate significant prying but not so much that it fails outright.
• By $t_f = 0.875$ in, the flange is stiff enough that prying drops to zero ($t_{min} \approx 0.85$ in for this geometry).
• The transition from "prying failure" to "prying-controlled design" to "no prying" occurs over a narrow thickness range (roughly 0.50 in to 0.875 in).
• The relationship is highly nonlinear. Doubling the flange thickness from 0.50 in to 1.00 in increases $M_p$ by 4x (proportional to $t_f^2$).

This nonlinearity means that modest increases in flange thickness often eliminate prying entirely, while modest decreases can cause a sudden catastrophic failure. Never interpolate prying behavior — calculate it explicitly.

Common Mistakes in Prying Design

1. Ignoring prying entirely. The single most common error. Engineers often check bolt tension capacity in isolation and assume the connection is adequate. If the flange or angle leg thickness is less than $t_{min}$, this assumption is unconservative — sometimes dangerously so.

2. Using the wrong b' dimension. The distance to the plastic hinge is not simply the gage distance. The hinge forms at the face of the stem (or web), not at the bolt centerline. Subtract half the bolt diameter and account for the k-dimension (or fillet radius) of the section.

3. Increasing bolt diameter to solve prying problems. Larger bolts have higher $T_u$, which increases $t_{min}$. Larger bolts make prying worse, not better. The correct response to a prying failure is to increase flange thickness, reduce the bolt gage, or add stiffeners.

4. Neglecting the tributary length p. For bolts arranged in a line, p is the bolt spacing. For a single bolt, p is limited to the effective flange width. Using an overestimated p (e.g., the full flange width instead of the bolt spacing) will underpredict prying forces.

5. Applying AISC tabular values to non-standard geometries. Tables 9-2 through 9-8 cover common WT, angle, and plate geometries. If your connection geometry does not match the tabulated assumptions (especially b' and a' values), the tables are not applicable. Use the analytical equations.

6. Confusing direct tension with total bolt tension. The bolt sees $T_{total} = T_{req} + Q$, not just $P_u / n_b$. The D/C ratio must be computed against $\phi T_u$ using the total, not the direct value.

FAQ

What is prying action in bolted connections?

Prying action is an additional tensile force that develops in bolts of a tension connection when the connected flange (or angle leg) deforms under load. As the flange bends, it levers against the bolt line, amplifying the bolt tension beyond the externally applied load. The prying force Q arises from the moment equilibrium of the T-stub flange and can increase the bolt tension demand by 30-60% or more, depending on the flange thickness-to-bolt-diameter ratio. This phenomenon is codified in AISC 360 Part 9 (p. 9-10 to 9-12) and EN 1993-1-8 Clause 6.2.4 (T-stub model).

How do you calculate prying force Q?

The prying force Q is calculated from T-stub flange equilibrium. Per AISC 360 Part 9: Q = (b'/a') _ (alpha _ delta * T_u - P_u/2), where b' is the distance from the bolt centerline to the plastic hinge at the stem face, a' is the distance from the bolt centerline to the plastic hinge at the flange tip, alpha is the moment ratio, delta is the net area ratio, T_u is the bolt nominal tensile strength, and P_u is the applied tension per bolt pair. Per EN 1993-1-8: the T-stub model uses three failure modes — complete flange yielding (Mode 1), combined flange yielding + bolt failure (Mode 2), and bolt failure only (Mode 3) — with the prying force implicitly included in Modes 1 and 2.

When can prying action be eliminated?

Prying action can be eliminated when the flange (or angle leg) is thick enough to prevent significant bending deformation. Per AISC 360 Part 9, the required flange thickness to eliminate prying is $t_{min} = \sqrt{(4 \cdot T_u \cdot b') / (p \cdot F_y)}$, where $T_u$ is the required bolt tension, $b'$ is the distance from bolt centerline to the stem face, $p$ is the tributary length of flange per bolt, and $F_y$ is the flange yield strength. For EN 1993-1-8, Mode 3 (bolt failure only) governs when the flange is sufficiently thick. Practical values: a flange gage-to-thickness ratio (g/t) below approximately 8-10 typically eliminates prying for common bolt grades and steel strengths.

Is this calculator a replacement for professional engineering judgment?

No — this is an educational reference only. All prying action calculations must be independently verified by a licensed Professional Engineer before use in any project. Results are PRELIMINARY — NOT FOR CONSTRUCTION.

Key Takeaways

• Prying force Q is additive to direct tension — bolts see $T_{req} + Q$, not just $P_u/n_b$. Ignoring Q can lead to bolt failure at loads well below the nominal capacity.
• Flange thickness is the primary defense against prying. A thicker flange increases $M_p$ (proportional to $t_f^2$), which rapidly reduces Q. Modest increases in $t_f$ can eliminate prying entirely.
• Larger bolts make prying worse. Increasing bolt diameter increases $T_u$, which increases $t_{min}$. If prying governs, make the flange thicker — not the bolts bigger.
• The lever ratio b'/a' matters. Push the bolts as close to the stem face as practical (minimize b') and provide adequate edge distance (maximize a') to reduce the prying contribution.
• AISC gives explicit Q; EN 1993 gives failure modes. AISC calculates prying force directly. Eurocode bakes prying into Mode 1 (full flange yield) and Mode 2 (combined flange + bolt failure), with Mode 3 being the no-prying case.
• The transition from "prying failure" to "no prying" is narrow. A 0.25-inch increase in flange thickness can take you from a failed connection to zero prying. Do not interpolate — calculate.

Run This Calculation

Bolted Connections Calculator — full bolted connection design including tension, shear, bearing, and prying action checks per AISC 360, EN 1993-1-8, AS 4100, and CSA S16. Enter your connection geometry and the calculator determines bolt tension demand including prying forces.

Bolt Torque Calculator — calculate the required pretension torque per AISC 360 J3.8 and AS 4100 Clause 15.2.5.2 for preloaded bolt assemblies in prying-sensitive connections.

Further Reading

• Steel Connection Design Guide — comprehensive connection design reference covering all joint types
• Steel Bolt Capacity Guide — AISC 360, EN 1993, AS 4100 — bolt shear, bearing, and tension capacity across all three major codes
• EN 1993-1-8 Steel Connection Design — Bolt & Weld Checks — Eurocode connection design with worked examples and gamma factor tables
• Base Plate Design Example — AISC 360, AS 4100, EN 1993 & CSA S16 — tension-side base plate prying checks for column anchorage
• Gusset Plate Design Guide — Whitmore Section, Block Shear, Buckling — bolted gusset plate design including tension and compression checks
• Fillet Weld Size Guide — weld sizing for stiffened and unstiffened flange connections
• Bolt spacing and edge distance requirements — minimum and maximum spacing for bolted tension connections
• Bolt hole sizes reference — standard, oversize, and slotted hole dimensions per AISC 360
• Steel Fy and Fu reference — yield and tensile strengths for flange materials across steel grades
• AISC 360 code notes — North American structural steel specification reference
• EN 1993 code notes — Eurocode 3 structural steel reference
• Disclaimer (educational use only)

Disclaimer (educational use only)

This page is provided for general technical information and educational use only. It does not constitute professional engineering advice, a design service, or a substitute for an independent review by a qualified structural engineer. Any calculations, outputs, examples, and workflows discussed here are simplified descriptions intended to support understanding and preliminary estimation.

All real-world structural design depends on project-specific factors (loads, combinations, stability, detailing, fabrication, erection, tolerances, site conditions, and the governing standard and project specification). You are responsible for verifying inputs, validating results with an independent method, checking constructability and code compliance, and obtaining professional sign-off where required.

The site operator provides the content "as is" and "as available" without warranties of any kind. To the maximum extent permitted by law, the operator disclaims liability for any loss or damage arising from the use of, or reliance on, this page or any linked tools.