Steel Tension Rods — Tie Rod, Hanger Rod & Sag Rod Design per AISC 360

Steel tension rods are round structural bars loaded in axial tension, typically threaded at one or both ends to accept clevises, turnbuckles, or nuts. They appear throughout steel construction under several names depending on application:

• Tie rods -- horizontal or diagonal members resisting outward thrust in arches, frames, and braced bays
• Hanger rods -- vertical members supporting gravity loads from floors, mezzanines, or piping
• Sag rods -- lightweight rods preventing purlins and girts from rolling under gravity component loads on sloped or vertical surfaces
• Brace rods -- diagonal tension-only members in lateral force-resisting systems

Design is governed by AISC 360-22 Chapter D (tension members) and Chapter J (threaded fastener provisions for the threaded portion). This page covers the governing limit states, provides capacity tables for common rod sizes, addresses accessory selection, and compares requirements across international codes.

Quick access:

• Rod material grades
• AISC Chapter D design
• Thread stress area table
• Capacity table -- A36 and A572 Gr 50
• Slenderness limit
• Turnbuckle and clevis selection
• Multi-code comparison
• Worked example
• Common mistakes
• FAQ

Rod material grades

F1554 Grade 36 is weldable without preheat. Grades 55 and 105 require preheat per AWS D1.1 if welding is involved. Grade 105 is quenched and tempered and must not be heated above 800 degF (425 degC) to avoid metallurgical damage. A449 rod is common in building construction for rod diameters 1/4" through 3" and provides a good balance of strength and ductility.

AISC Chapter D design -- tensile capacity

AISC 360-22 Chapter D requires checking two limit states for tension members. The design strength is the lesser of the two:

Limit state 1: Yielding on the gross area

phiPn = 0.90 * Fy * Ag

Where Ag = pi/4 * db^2 (gross area based on nominal rod diameter). This limit state prevents excessive elongation of the rod under service loads. It applies to the unthreaded (shank) portion.

Limit state 2: Rupture on the effective net area

phiPn = 0.75 * Fu * Ae

Where Ae = effective net area. For a threaded rod, Ae equals the tensile stress area At of the threads. This limit state prevents fracture at the reduced threaded cross-section.

The tensile stress area accounts for the thread root diameter rather than the nominal diameter:

At = 0.7854 * (D - 0.9743 / n)^2

Where D = nominal rod diameter (inches) and n = number of threads per inch (UNC series). This formula is derived from the mean of the pitch and minor diameters and is the standard area used in threaded fastener design.

Which limit state governs?

The governing capacity is the lesser of yielding and rupture. For threaded rods, rupture on the net area almost always governs because:

• At/Ag ranges from 0.72 to 0.80 for standard UNC threads
• The ratio (0.75 _ Fu) / (0.90 _ Fy) must exceed At/Ag for yielding to govern
• For A36 (Fu/Fy = 58/36 = 1.61): (0.75 _ 58) / (0.90 _ 36) = 1.34, which is greater than At/Ag for most sizes, so rupture still governs for smaller diameters
• For A572 Gr 50 (Fu/Fy = 65/50 = 1.30): (0.75 _ 65) / (0.90 _ 50) = 1.08, which is less than At/Ag -- rupture governs for all sizes

For unthreaded rod (or rod with threads excluded from the critical section), only yielding on the gross area is checked. This is common in hanger rods where nuts bear on a plate and the critical section is in the unthreaded shank.

Thread tensile stress area table

The following table provides tensile stress areas for Unified National Coarse (UNC) threads, the standard thread series used for structural rods in North America.

For 8-thread series (8N) rods used on larger diameters, substitute n = 8 in the At formula. Some engineers specify 8-thread series on rods 1" and larger for easier field engagement.

Capacity table -- A36 and A572 Gr 50

The following tables provide design tensile capacities (phiPn, kips) for common rod sizes under AISC 360-22. Values are for LRFD. The governing capacity (minimum of yielding and rupture) is shown.

A36 (Fy = 36 ksi, Fu = 58 ksi)

A572 Grade 50 (Fy = 50 ksi, Fu = 65 ksi)

For unthreaded rods, only yielding on the gross area is checked (phi = 0.90). For threaded rods, rupture on the tensile stress area (phi = 0.75) governs in every case shown. This confirms the general rule: always check the threaded section -- it will almost always control.

Slenderness limit L/r <= 300

AISC 360-22 Section D1 recommends a maximum slenderness ratio of L/r = 300 for tension members. This is a serviceability recommendation, not a strength requirement. Exceeding L/r = 300 does not reduce the design tensile capacity, but it may result in:

• Excessive sag under self-weight
• Visible vibration or flutter under wind loads
• Difficulty in erection and pretensioning
• Perceived lack of rigidity by building occupants

For a round rod, the radius of gyration is r = D/4. The slenderness check becomes:

L/r = 4L / D <= 300

Where L is the length between lateral supports or end connections, and D is the nominal rod diameter. Solving for minimum diameter:

D >= 4L / 300 = L / 75

Example: For a 12 ft (144 in) long rod, the minimum diameter to satisfy L/r = 300 is D >= 144/75 = 1.92". A 2" rod meets the limit; a 1-3/4" rod (L/r = 329) exceeds it. Engineers may accept the exceedance for non-critical members, particularly sag rods, but should document the decision.

For pretensioned rod systems (tie rods with turnbuckles), the pretension force eliminates sag and significantly improves the effective stiffness. Many engineers treat the L/r = 300 limit as a guideline for these systems rather than a hard requirement.

Turnbuckle and clevis selection

Turnbuckles provide length adjustment and pretensioning capability. Clevis-type end fittings allow pin connections at rod ends. When specifying these accessories:

Turnbuckles

• Turnbuckle capacity must equal or exceed the rod design capacity. AISC Manual Table 15-3 lists rated capacities for standard turnbuckle sizes.
• Take-up length is typically 6" (150 mm) total (3" per side). Specify longer turnbuckles for installations requiring more adjustment range.
• Body type: Open-body turnbuckles allow visual inspection of thread engagement. Closed-body turnbuckles provide better corrosion protection.
• Minimum thread engagement: At least 1.5 times the rod diameter of thread engagement into the turnbuckle body at each end is recommended. Full engagement (thread visible through the open body) is preferred.

Clevises and pins

• Clevis capacity must match or exceed the rod capacity. AISC Manual Table 15-2 provides clevis ratings by size designation (2 through 8).
• Pin check: Verify pin shear (double shear per AISC Chapter J), pin bearing on the clevis ear, and pin bending between clevis ears.
• Net section of clevis ear: Check tension rupture on the net section through the pin hole per AISC 360 Section D5, which provides specific provisions for pin-connected tension members.
• Pin diameter should be specified to match the clevis -- do not use undersized pins.

Other end fittings

• Coupler nuts (sleeve nuts) join two threaded rods end-to-end. Minimum engagement length must equal or exceed the standard nut height (approximately 0.875 * D for heavy hex nuts).
• Welded attachments: Rods may be welded to base plates or gussets, but only if the rod material is weldable (A36, A572) and proper weld procedures are followed. F1554 Grade 105 is not weldable.
• Bearing plates: Where a rod passes through a steel beam or column, provide a bearing plate or washer on each side to distribute the rod force.

Multi-code comparison -- AS 4100 and EN 1993

Tension rod design follows similar principles across international standards, but capacity reduction factors and terminology differ.

AS 4100 (Australia) -- Tension members

AS 4100 Clause 7.2 checks two limit states analogous to AISC Chapter D:

• Yield on gross section: phi _ Nt = 0.90 _ Ag * fy (identical phi to AISC)
• Fracture on net section: phi _ Nt = 0.90 _ k*r * An _ fu, where k_r is a reduction factor for non-uniform stress distribution (typically 0.85 for bolted/ threaded connections)
• Note: AS 4100 applies phi = 0.90 to both limit states (AISC uses 0.75 for rupture). Thread stress areas are calculated per AS 1275 (metric thread standard).

The Australian standard also requires a ductility check: Ag _ fy / (An _ fu) <= 1.0, ensuring yielding precedes fracture for robust behavior. This is not an explicit AISC requirement but is satisfied implicitly when rupture governs.

EN 1993-1-1 (Eurocode 3) -- Tie rods

EN 1993-1-1 Clause 6.2.3 checks tension resistance as:

• Plastic resistance: Nt,Rd = Ag * fy / gamma_M0 (gamma_M0 = 1.0)
• Ultimate resistance: Nt,Rd = 0.9 _ An _ fu / gamma_M2 (gamma_M2 = 1.25)
• The design resistance is the lesser of the two. The factor 0.9 * An accounts for the effective net area, and An for threads is defined per EN 1090-2.

For European projects, common rod materials are S235 (fy = 235 MPa, fu = 360 MPa) and S355 (fy = 355 MPa, fu = 510 MPa), which are roughly equivalent to A36 and A572 Gr 50, respectively.

Comparison summary

The most significant difference is in the rupture resistance factor: AISC applies phi = 0.75 (lower capacity), while AS 4100 applies phi = 0.90 with a k_r reduction. EN 1993 uses gamma_M2 = 1.25 (equivalent to phi = 0.80). For the same rod geometry and material, AISC will generally produce the most conservative (lowest) threaded capacity.

Worked example -- 1-1/4" A36 rod

Problem: Design a 1-1/4" diameter A36 tie rod (Fy = 36 ksi, Fu = 58 ksi) spanning 12 ft between connection points. The rod is threaded both ends with UNC threads (7 threads per inch) and fitted with turnbuckles. Determine the design capacity and check the slenderness ratio.

Step 1 -- Material properties and geometry:

• Fy = 36 ksi (248 MPa), Fu = 58 ksi (400 MPa)
• D = 1.25" (31.8 mm)
• L = 12 ft = 144 in (3658 mm)
• Threads: 7 UNC per inch
• Ag = pi/4 * (1.25)^2 = 1.227 in^2

Step 2 -- Thread tensile stress area:

At = 0.7854 * (D - 0.9743/n)^2
At = 0.7854 * (1.25 - 0.9743/7)^2
At = 0.7854 * (1.25 - 0.1392)^2
At = 0.7854 * (1.1108)^2
At = 0.7854 * 1.2339
At = 0.969 in^2

Step 3 -- Yielding on gross area (Limit State 1):

phiPn = 0.90 * Fy * Ag = 0.90 * 36 * 1.227 = 39.8 kips (177 kN)

Step 4 -- Rupture on effective net area (Limit State 2):

phiPn = 0.75 * Fu * At = 0.75 * 58 * 0.969 = 42.1 kips (187 kN)

Wait -- yielding governs at 39.8 kips, not rupture. This happens because A36 has a high Fu/Fy ratio (1.61), making yielding critical for this particular diameter. Double-check: 0.75 _ 58 / (0.90 _ 36) = 43.5/32.4 = 1.34, and At/Ag = 0.969/1.227 = 0.79. Since 1.34 > 0.79, yielding is expected to be close to or governing.

Result: Design capacity = 39.8 kips (177 kN).

Step 5 -- Slenderness check:

r = D/4 = 1.25/4 = 0.3125 in
L/r = 144 / 0.3125 = 461 > 300 -- exceeds recommended limit

This rod exceeds the L/r = 300 serviceability limit. Options:

1. Increase diameter to 2" (L/r = 288, within limit)
2. Provide intermediate lateral support (e.g., a guide bracket at mid-span)
3. Document the exceedance and specify pretensioning via the turnbuckle to control sag

For this example, the engineer selects option 3: pretension the rod to approximately 5% of capacity (2 kips) via the turnbuckle to eliminate visible sag, and documents the slenderness exceedance as acceptable for a tension-only member.

Step 6 -- Turnbuckle selection:

Per AISC Manual Table 15-3, a 1-1/4" turnbuckle has a rated safe working load exceeding 42 kips, which covers the rod capacity of 39.8 kips. Specify an open-body turnbuckle for inspection.

Step 7 -- Clevis selection (if applicable):

If clevis end fittings are used, select a size from AISC Manual Table 15-2 with a capacity equal to or exceeding 39.8 kips. A No. 3 clevis (rated approximately 37 kips) is marginally insufficient; a No. 3.5 or No. 4 clevis is required.

Sag rod design

Sag rods support purlins against rolling and carry a component of the gravity load parallel to the roof slope. For a roof slope of theta degrees:

T_sag = w_purlin * L_purlin * sin(theta) / n_sag_rods

Where w_purlin = purlin dead load per foot, L_purlin = purlin span, and n_sag_rods = number of sag rods in the purlin span. Place sag rods at the ridge (where they anchor to a ridge beam) and at intermediate panel points.

Each sag rod in a bay must carry the accumulated load from all purlins below it up to the ridge. The topmost sag rod (nearest the ridge) carries the largest force. For typical metal building roof slopes of 1/4:12 to 1:12, the sag rod forces are small, and 5/8" or 3/4" rods usually suffice. However, for steeper slopes or heavy cladding, the analysis must be performed.

Sag rods are typically not pretensioned -- they are installed snug-tight. Sag rod design is often governed by the minimum practical diameter for handling (5/8" or 3/4") rather than by stress limits.

Common mistakes

1. Using gross area instead of tensile stress area for threaded sections. Threads reduce the effective area by 20--28%. Using Ag instead of At overestimates capacity by that amount. Always use At from the thread stress area table for threaded portions.

2. Not checking connection fitting capacities. Turnbuckle bodies, clevis pins, coupler nuts, and threaded eye rods all have rated capacities that may be lower than the rod itself. The system capacity is controlled by the weakest component.

3. Heating quenched-and-tempered rods for bending. F1554 Grade 105 and A193 B7 rods lose their strength if heated above 800 degF (425 degC). Field bending or welding of these grades is not permitted without engineering review and potential re-heat-treatment.

4. Omitting corrosion protection on threaded surfaces. Exposed tension rods (especially sag rods in humid or industrial environments) require hot-dip galvanizing or painting. Threaded surfaces are especially vulnerable because the thread crevices trap moisture. Galvanizing must be done after threading to coat the threads.

5. Not accounting for prying action. When tension rods attach to flexible base plates, angles, or flanges, prying action can amplify the rod tension by 20--40% above the applied load. This is particularly critical for hanger rods connected to thin base plates.

6. Ignoring installation tolerances. Rods fabricated too short cannot be connected; rods too long may not allow adequate thread engagement into turnbuckles. Specify rod length tolerances (typically +0/-1/4") and require mock-up assembly verification for critical applications.

7. Specifying left-hand threads without clear notation. Turnbuckles require one right-hand and one left-hand thread to function. If the left-hand thread is not clearly specified on shop drawings, fabricators may supply all right-hand threads, making the turnbuckle inoperable.

8. Failing to check rod elongation under service loads. For long tie rods in structures sensitive to movement (e.g., glass curtain wall supports, precision equipment supports), the elastic elongation under service load may exceed deflection limits. Elongation = PL/(AE). For a 1" A36 rod at 20 kips service load over 20 ft: elongation = 20000 _ 240 / (0.785 _ 29000) = 0.21", which may be unacceptable for deflection-sensitive supports.

Frequently asked questions

What is the difference between a tie rod and a hanger rod? A tie rod resists horizontal or diagonal tension forces (e.g., resisting outward thrust in an arch or frame), while a hanger rod resists vertical tension from gravity loads (e.g., supporting a mezzanine floor beam from the roof structure above). Both are designed using the same AISC Chapter D provisions, but hanger rods typically require more attention to connection details and prying action.

Do I need to check shear in a tension rod? Pure tension rods carry axial tension only and do not require a shear check. However, if the rod is subject to combined tension and shear (e.g., a diagonal brace rod that also resists a gravity component), or if the rod passes through a shear plate, the interaction must be evaluated. For most tie rods and hanger rods, shear is negligible.

What phi factor should I use for threaded rod tension? Per AISC 360-22, use phi = 0.90 for yielding on the gross area and phi = 0.75 for rupture on the net (threaded) area. These correspond to the resistance factors for tension members in Table D3.1. The lower phi for rupture reflects the more sudden and less ductile nature of tensile fracture compared to yielding.

Can tension rods resist compression? Tension rods have negligible useful compression capacity due to their extremely high slenderness. A 1" diameter rod at 20 ft has L/r = 960, far beyond any reasonable compression limit. If the member must resist load reversal, use a crossed-rod system (only the tension rod in each diagonal is active), or replace the rod with a wide-flange or HSS member capable of handling compression.

What is the minimum thread engagement length for a threaded rod? The minimum thread engagement should provide a tensile capacity through the threads equal to or exceeding the rod capacity. As a practical rule, engagement length should be at least 1.0 times the rod diameter (1.0D) for standard nut applications, and 1.5D for critical connections. AISC Section J3.1 provides thread stripping provisions that can be checked if the engagement is marginal.

How do I select a turnbuckle size? Match the turnbuckle size to the rod diameter. AISC Manual Table 15-3 lists standard turnbuckle sizes and their rated capacities. The turnbuckle safe working load must equal or exceed the rod design capacity. For example, a 1-1/4" rod requires a 1-1/4" turnbuckle, which has a rated capacity exceeding the rod's design strength.

Should sag rods be designed for the full roof slope component? Sag rods carry only the component of purlin dead load parallel to the roof slope, which is typically small for low-slope roofs (1/4:12 to 1:12). The topmost sag rod nearest the ridge carries the accumulated load from all purlins below. In practice, sag rod size is usually governed by minimum practical diameter (5/8" or 3/4") rather than by stress. For slopes steeper than 4:12, explicit calculation is warranted.

Can I weld a threaded rod end to a base plate instead of using nuts? Yes, but only if the rod material is weldable. A36 and A572 rods are weldable. F1554 Grade 105 and A193 B7 are quenched and tempered and must not be welded without special procedures and engineering approval. When welding, develop the weld to transfer the full rod capacity, and check the base plate for punching shear and bending.

Run this calculation

Use the Steel Calculator tools to run tension rod design checks with full AISC 360 compliance:

• Bolted Connections Calculator -- for threaded fastener checks on rod ends
• Base Plate Design Calculator -- for hanger rod connections to base plates
• Section Properties Database -- look up cross-sectional properties for rod sizes
• Steel Connection Types -- understand connection options for tension members

Related references

• Steel Connection Types -- overview of welded, bolted, and pinned connections
• Bolt Grades Reference -- material grades and capacities for high-strength bolts
• Base Plate Design -- design of column and hanger base plates
• Diagonal Bracing -- lateral bracing systems using tension rods
• Welded Connections -- welded attachments for rod end connections
• How to Verify Calculations -- quality assurance procedures for steel design
• Steel Design Codes Overview -- comparison of AISC, AS 4100, EN 1993, and CSA S16
• Structural Steel Grades -- material properties for common structural steels
• Anchor Bolt Design -- anchor rod design per ACI 318

Disclaimer

This page is for educational and reference use only. It does not constitute professional engineering advice. All design values must be verified against AISC 360-22 Chapters D and J and the governing project specification. Capacity table values are approximate and should be independently confirmed. The site operator disclaims liability for any loss, damage, or injury arising from the use of this information. Structural design must be performed by or under the supervision of a licensed professional engineer.