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10

Plate Girders

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Why Structural Steel?

Built-up I-sections, tension-field action, stiffener design.

⏱ 120 min★ Advanced✎ 3 objectives
§01Section 01

Engineering story

Engineering story
Chapter 10 · Plate Girders

Built-up I-sections, tension-field action, stiffener design.

A real project narrative for this chapter will be authored as this chapter migrates to the v3.0 structured schema.

§02Section 02

Learning objectives

After this chapter you will be able to
  • Design a built-up I-section
  • Evaluate tension-field action
  • Detail transverse stiffeners
§03Section 03

Engineering motivation

§04Section 04

Failure mechanisms

Failure mechanisms & lessons learned

Photographs and lessons-learned case studies for this topic will be added during chapter migration.

AISC Reference Box
  • AISC 360-22 — Specification chapter governing this topic
  • AISC Manual 16th Ed. — Design tables and worked examples

Why This Chapter Matters

When a rolled W-shape is not deep enough, a built-up I-girder is welded from plates. Plate girders open up tension-field action, stiffener design, and flange-web proportioning issues that don't arise in rolled shapes.

Learning Objectives

  • Proportion a plate girder to minimize weight for a given moment demand.
  • Design transverse and bearing stiffeners per AISC G2.3 and J10.
  • Compute tension-field capacity Vn per AISC G2.2.
  • Check flange local buckling, web local buckling, and web sidesway buckling.
  • Detail full-penetration welds joining flanges to web.

Where This Chapter Is Used

Long-span bridge girders, industrial crane runways, and heavy-transfer girders in commercial buildings.

ANSI / AISC 360-22Specification for Structural Steel Buildings16.1-70 to 16.1-100
Chapter
F
AISC 360-22

Chapter F. Design of Members for Flexure — §F5 & F13 (Built-Up Girders)

Use this reference to flip directly to the correct page of the AISC 360-22 Specification while solving problems in this course chapter.

§Section titlePage
F5Doubly Symmetric I-Shapes with Slender Webs (Plate Girders)16.1-70
F13Proportions of Beams and Girders (Flange/Web Proportions)16.1-90
G2.2Tension-Field Action (Post-Buckling Shear)16.1-103
G2.3Transverse Stiffeners16.1-104
J10Bearing Stiffener Design16.1-146

Companion reference: AISC Design Guide 25 — Plate Girders

Lecture Notes

Chapter 10 — Plate Girders (AISC 360-22 §F5, §G2.2)

Chapter focus. When a rolled W-shape can't span far enough or deep enough — long-span industrial floors, crane runways, bridge girders — engineers weld up a plate girder: a slender web plate + two thick flanges. Slender webs need special flexural and shear provisions (AISC §F5, §G2.2) and often need bearing / intermediate stiffeners.

1. When Plate Girders Are Needed

When rolled W-shapes cannot span the required distance or moment, engineers weld plates into an I-shape. The classifying dimension is the web slenderness:

λw = h / tw    vs    λrw = 5.70 √(E / Fy)

If h/tw > λrw the section is a slender-web plate girder governed by §F5 (flexure) and §G2.2 (shear with tension-field action).

2. Nominal Flexural Strength — §F5

Eq. F5-1 compression-flange yieldingMn = Rpg · Fy · Sxc
Eq. F5-6 bend-buckling reductionRpg = 1 − [ aw / (1200 + 300·aw) ]·( hc/tw − 5.7√(E/Fy) ) ≤ 1.0
aw = hc·tw / (bfc·tfc) ≤ 10

Also check LTB (F5-2), compression-flange local buckling (F5-3), tension-flange yielding (F5-4).

3. Shear — Tension-Field Action (§G2.2)

Eq. G2-7Vn = 0.6 Fy Aw [ Cv2 + (1 − Cv2) / (1.15·√(1 + (a/h)²)) ]
  • TFA permitted only when 2·Aw/(Afc+Aft) ≤ 2.5 and h/bfc, h/bft ≤ 6.0.
  • End panels and panels adjacent to holes: NO tension-field — use §G2.1 (Cv1 only).

4. Transverse Stiffeners (§G2.3)

Ist ≥ b·tw³·j, j = 2.5/(a/h)² − 2 ≥ 0.5

Stiffener spacing a/h ≤ [ 260 / (h/tw) ]² ≤ 3.0 to enable tension-field.

5. Design Workflow

  1. Set web h, tw; check h/tw ≤ 260 and vs 5.7√(E/Fy).
  2. Compute aw, Rpg, φMn; verify ≥ Mu.
  3. Layout stiffeners at ends and at concentrated loads.
  4. Check panel shear φVn ≥ Vu per panel.
  5. Detail bearing stiffeners at reactions (§J10).

Additional Design Aids & Stratified Equations

Plate girder — transverse stiffener layout a (end panel — no TFA) a (interior — TFA OK) a a (end panel — no TFA) h (web depth)
End panels (adjacent to supports) may NOT use tension-field action; interior panels may.
Panel aspecta/h ≤ (260/(h/t_w))² ≤ 3.0
Stiffener moment of inertiaI_st ≥ b · t_w³ · j, j = 2.5/(a/h)² − 2 ≥ 0.5

⚠ Common mistakes

  • Applying tension-field action to end panels (never allowed).
  • Using Rpg = 1 without checking hc/tw vs 5.7√(E/Fy).
  • Missing the aw ≤ 10 cap.
  • Forgetting bearing stiffeners under concentrated loads.

🎞 Watch the Phenomenon — Loading Stages

Slender web plate under axial / shear compression σ σ
Slender web plate under compression / shear — flat, wave, buckle, post-buckling.
StageWhat is happening in the animation
1 — Flat / elastic (σ < Fcr)Plate carries uniform in-plane stress. Any minor out-of-flatness is negligible.
2 — Onset of waveVery small out-of-plane wave becomes visible near the critical stress. The plate is behaving like a wide, thin column that hasn't quite buckled.
3 — Elastic plate bucklingσcr = kπ²E / [12(1−ν²)(b/t)²]. Plates buckle into waves, not a single half-sine, because the edges are supported.
4 — Post-buckling resistanceUnlike columns, plates can carry more load after buckling — the edges keep supporting the flow of stress. Effective-width method (AISC E7) uses this.
5 — Yielding of edge strips / crushingUltimate failure is when the edge strips finally yield. This is why HSS wall slenderness and web h/tw get so much attention.

📖 Using the AISC Manual — Plate Girders

Companion reference: Chapter F13 / G — no dedicated selection tables (built-up sections). In practice, engineers rarely compute every quantity from first principles — the AISC Steel Construction Manual (16th Ed.) tabulates φRn (or Rn/Ω) for every rolled shape so you can pick a member in seconds. Formulas remain essential for understanding, verifying, and for anything the tables do not cover.

Because plate girders are custom-fabricated, the Manual does not tabulate φMn or φVn — you must compute from Chapter F13 (flexure with slender web) and G2.2 (tension-field action) directly. However, two aids help:

  • Manual Part 1 lists standard plate thicknesses and widths available from mills — always specify a stocked size.
  • Design Guide 25 (Frame Design Using Web-Tapered Members) gives complete worked examples for the girder + stiffener check sequence.
Table vs. formula — which to use? Use tables to select a shape quickly. Use formulas to verify odd geometry, non-standard grades (Fy≠50 ksi), unusual K-factors or Lb, and to answer exam problems that hand you a section not in the current Manual.
Welded plate girder (stiffeners shown)
Welded plate girder with intermediate transverse stiffeners and tension-field action (AISC Ch. F + App. 6).

Formula Sheet

NameEquationAISC Ref
Design strengthφ Rn ≥ RuAISC 360-22 B3.1

Worked Example

Worked Example 10.1 — Plate-Girder Flexure Check

Given

  • Welded plate girder, A572 Gr. 50 (Fy = 50 ksi).
  • Web: h = 60 in, tw = 3/8 in → h/tw = 160.
  • Flanges: bf = 16 in, tf = 1 in.
  • Mu = 3200 k-ft; compression flange continuously braced by deck (Lb ≈ 0).
Welded plate girder — F5 slender-web flexure b_f = 16″ t_f = 1″ h = 60″ h/t_w = 160 t_w = 3/8″ C T S_xc = I_x / c ; R_pg = 1 − [a_w/(1200+300 a_w)]·(h/t_w − 5.7√(E/F_y))
Figure 10.1a — Welded plate-girder cross-section with F5 stress distribution

Step 1 — Slender-Web Check

§F5 thresholdh/tw > 5.70 √(E/Fy) ⇒ slender-web plate girder
5.70·√(29000/50) = 137.2 < 160 → slender-web plate girder → §F5.

Step 2 — Section Properties

FormulasAfc = bf·tf ;  Aw = h·tw ;  Ix = 2·Af·yf² + tw·h³/12 ;  Sxc = Ix/(h/2 + tf)
Afc = Aft = 16·1 = 16 in². Aw = 60·0.375 = 22.5 in².
Ix ≈ 2·[16·(30.5)²] + 0.375·60³/12 = 29,768 + 6,750 = 36,518 in⁴.
Sxc = Ix / (h/2 + tf) = 36,518 / 31 = 1,178 in³.

Step 3 — aw and Rpg

Eq. F5-6 / F5-1aw = Aw/Afc ≤ 10 ;  Rpg = 1 − [aw/(1200 + 300 aw)]·(h/tw − 5.7√(E/Fy)) ≤ 1
aw = 22.5/16 = 1.406 ≤ 10 ✓
Rpg = 1 − [1.406/(1200+300·1.406)]·(160 − 137.2) = 1 − (1.406/1621.8)·22.8 = 1 − 0.0198 = 0.980

Step 4 — φMn

Eq. F5-1Mn = Rpg·Fy·Sxc ;  φMn = 0.90 Mn
Mn = 0.980·50·1178 / 12 = 4,809 k-ft
φMn = 0.90·4809 = 4,328 k-ft ≥ 3200 ✓
Utilization 3200/4328 = 0.74 → OK. Next: shear panels and intermediate stiffeners.

FE-Style Worked Examples(6)

Each example mirrors the NCEES FE Civil Reference Handbook style: brief givens, a labeled figure, AISC section reference, step-by-step numeric solution, and a single boxed answer.

Given
Span 80 ft, gravity wu=4 k/ft, no rolled W deep enough/economical.
AISC Reference
AISC Ch. F + App. F13
Step-by-step solution
  1. Decision
    Built-up I with h/tw > 260 → plate girder territory.
Answer Use welded plate girder, design per §F13.
Bend the rules: when to use a plate girder
Problem statement image
Welded plate girder (stiffeners shown)
DIMDimensions from the problem statement
wu = 4k
Plate girder — flange + web dimensions
  • Web h × t_w (slender if h/t_w > 5.7√(E/F_y))
  • Flange b_f × t_f (compact / non-compact / slender per B4.1)
  • Transverse stiffeners at spacing a control web shear

Graded Chapter Quiz(13 FE-style questions · AISC Manual required)

These questions reference AISC Steel Construction Manual (16th ed.) — sections, equations, and tables are cited explicitly. Use a calculator. Each question offers a clue you may reveal before answering. Submissions are recorded to your account once signed in.

C10-01AISC 360-22 Table B4.1b Case 15
1. Plate girder web is classified 'slender' when h/tw exceeds:
Welded plate girder h/tw stiff. web tw flange PL
C10-02AISC 360-22 §F5
2. §F5 gives Mn for slender-web I-shape as controlled by:
Welded plate girder h/tw stiff. web tw flange PL
C10-03AISC 360-22 Eq. F5-6
3. Bending strength reduction Rpg for slender web:
C10-04AISC 360-22 §G2.2
4. Tension-field action (TFA) uses:
C10-05AISC 360-22 §G2.2(b)
5. TFA not permitted in:
C10-06AISC 360-22 §G2.2
6. Intermediate stiffener spacing recommended a/h:
Welded plate girder h/tw stiff. web tw flange PL
C10-07AISC 360-22 Eq. G2-13
7. Stiffener area required (Ast) per Eq. G2-13:
C10-08AISC 360-22 §J10
8. Bearing stiffeners are required at:
C10-09AISC 360-22 §F5
9. Flange local buckling (FLB) for slender-web girder governs when:
C10-10AISC 360-22 §F5
10. aw (web-to-flange ratio) =
C10-11AISC 360-22 §J1
11. Girder web splice designed for:
C10-12AISC 360-22 §F5 & Comm.
12. Hybrid girder (flange Fy > web Fy) requires:
C10-13AISC 360-22 Eq. G2-6
13. For a girder h/tw=200, Fy=50, a/h=2, kv from AISC:
Welded plate girder h/tw stiff. web tw flange PL
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Your file — PDF, Word document, scanned handwriting or a photo — is read page by page like an experienced structural engineering instructor would. The scan is validated first, then your reasoning, structural model, calculations, diagrams, code basis and final answers are graded on process, not just the final number. Design work is additionally reviewed against AISC 360-22 and ACI 318-19. Partial credit applies, and one early mistake carried correctly forward is only penalized once.

Before you attach the file
  • Include every page, in order and right way up — a missing page cannot earn credit.
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  • Write in dark pen; faint pencil is the most common 'UNREADABLE — INSTRUCTOR REVIEW REQUIRED' flag.
  • Include all diagrams, FBDs, shear/moment diagrams and section sketches — label them.
  • Number each question the same way the assignment does, and note anything you skipped.
  • Show units on every line and box your final answers.
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§11Section 11

Chapter summary

Formula sheet
  • Design strength
    φ Rn ≥ Ru
    AISC 360-22 B3.1
Engineering checklist
  • Module 10: Plate Girders
  • Key limit states and AISC references are listed in the reference box.
  • Use φRn ≥ Ru for every check.
  • Verify section properties with the official AISC Manual.
Professional tips
  • • Mixing ASD and LRFD load combinations in the same problem.
  • • Using nominal strength Rn instead of design strength φRn.
  • • Forgetting to check every limit state listed in the AISC chapter.
§13Section 13

FE exam preparation

FE exam preparation
Concept review
Concept summary coming soon.
Calculator tips

Calculator tips coming soon.

Common exam traps

Traps coming soon.

Time management

Aim for ~3 minutes per FE problem; skip and return to any item that takes longer than 5 minutes.