Structural Steel Design · Study · PE Civil: Structural · FE → PE Prep
Structural Steel Design
9% of exam
AISC tension, compression, flexure, and shear member strength by LRFD and ASD, block shear, lateral-torsional buckling, beam-column interaction, and composite-beam behavior.
7 concepts
A. Horizontal members (beams, slabs)
AISC Flexure, Plastic Moment & LTB
The plastic moment Mp = Fy·Zx, the three lateral-torsional-buckling zones set by Lp and Lr, the moment-gradient factor Cb, compactness checks, and φb = 0.90.
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AISC Beam Shear & Web Strength
Web shear strength Vn = 0.6·Fy·Aw·Cv1, the φv = 1.00 break for rolled I-shapes, web local yielding and crippling under concentrated loads, and when stiffeners are needed.
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Using the AISC Manual Tables (Exam Strategy)
Navigate the 15th-ed Manual design tables — Zx (3-2), φcPn (4-1), available moment vs. Lb (3-10), φvVn — to read φ-strengths directly and beat the equations on the clock.
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B. Vertical members (columns, walls)
AISC Compression Member Strength
Compute the flexural-buckling strength of a steel column from KL/r: the elastic Fe, the inelastic/elastic Fcr branches at the 4.71 transition, and the LRFD/ASD strengths.
A steel column rarely fails by crushing — it fails by buckling, and the whole of AISC compression design is an answer to one question: how much does buckling knock the strength below the squash load FyAg? The PE Civil Structural exam tests this in the vertical-members area as a near-certain question, and the moves are always the same: find the governing effective slenderness KL/r, decide which buckling branch you are on, read or compute the critical stress Fcr, and apply the resistance or safety factor. The NCEES PE Civil Reference Handbook gives you no column-strength table — §4.2 Steel covers only fastener-group geometry and weld symbols — so this is a fully NARRATIVE topic taught from AISC 360-16 Chapter E and the Steel Construction Manual, 15th ed. (Table 4-1).
Slenderness governs everything
The effective slenderness ratio KL/r is the master variable. K is the effective-length factor that captures end restraint (the ideal pinned-pinned column is K=1.0; fixed-fixed is 0.5; a sway column with one end free can be 2.0
The elastic buckling stress Fe
The elastic critical stress is the Euler stress written in terms of slenderness — the stress at which a perfectly straight elastic column would buckle. It depends only on the modulus and the slenderness, never on Fy, because an elastic buckle happens before any yielding. Everything downstream — the branch decision, the inelastic reduction — is built on Fe, so compute it first and carry full precision.
Fe=(KL/r)2π2E
Two branches: inelastic vs. elastic buckling
Real columns have residual stresses and initial crookedness, so AISC splits the strength curve at KL/r=4.71E/Fy
Nominal strength and the design check
Once Fcr is known, the nominal compressive strength for the flexural-buckling limit state is simply the critical stress acting over the gross area Ag (net area never governs compression because the bolts are still there to carry load). Then apply the format you are working in — never mix them. In LRFD the design strength is ϕcPn
Local buckling and other limit states
The flexural-buckling equations above assume the cross-section's plates do not buckle locally before the member does — i.e., the section is nonslender. For nonslender elements (most rolled W-shapes used as columns, which AISC Table 1-1 confirms), use Ag as above. If any element is slender (high b/t), Chapter E reduces the strength through an effective-area factor and the section can lose capacity well below FyAg
Reading it straight from Manual Table 4-1
On the exam the fast path is almost always AISC Manual Table 4-1, which tabulates ϕcPn (and Pn/Ωc
Exam strategy
Work in this fixed order: (1) get both KxLx/rx and KyLy/ry
•Using the strong-axis rx when the weak axis controls. For a W-shape with equal bracing both ways, the smaller ry gives the larger KL/r
References
AISC 360-16 — Specification for Structural Steel Buildings, Chapter E (Design of Members for Compression) — Eqs. E3-1 through E3-4 and the 4.71√(E/Fy) transition.
AISC Steel Construction Manual, 15th ed. — Table 4-1 (Available Strength in Axial Compression) — Tabulated φcPn and Pn/Ωc vs. KL about the y-axis for Fy = 50 ksi.
NCEES PE Civil Reference Handbook v2.2 — §4.2 Steel — Confirms the handbook supplies no compression-strength method; topic is taught from AISC 360-16.
AISC Beam-Column Interaction
The H1-1a/H1-1b axial-flexure interaction equations, biaxial bending, in-plane vs. out-of-plane checks, and second-order amplification of moments via B1 and B2.
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C. Systems (trusses, frames, composite)
AISC Tension Members & Block Shear
Gross-section yielding vs. net-section rupture, the shear-lag factor U and effective net area, and block-shear rupture at bolted/welded end connections.
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Composite Steel Beams
Steel beam acting compositely with a concrete slab via shear studs: effective width, the plastic neutral axis from force balance, Mn, full vs. partial composite action, and stud strength.
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or more),
L
is the unbraced length, and
r=I/A
is the radius of gyration about the buckling axis. A column can have a different unbraced length and a different
r
about each principal axis, so you must check both axes and let the larger
KL/r
govern — that is where most exam errors hide. For a doubly-symmetric W-shape with equal bracing on both axes, the weak (minor,
y
) axis with the smaller
ry
always controls.
(rKL)gov=max[rxKxLx,ryKyLy]
(equivalently
Fy/Fe=2.25
). Stocky columns below that limit buckle inelastically — partial yielding precedes buckling — and use the transcendental
0.658
form, which smoothly approaches
Fy
as the column gets stubby. Slender columns above the limit buckle elastically, and
Fcr
is simply
0.877Fe
, the
0.877
accounting for out-of-straightness. Pick the branch by comparing
. Singly-symmetric, unsymmetric, and slender built-up shapes may also be governed by torsional or flexural-torsional buckling rather than pure flexural buckling — but for the doubly-symmetric rolled shapes the PE favors, minor-axis flexural buckling controls.
Limit = 113 for Fy=50 ksi, 134 for Fy=36 ksi. At or below: inelastic branch; above: elastic branch.
Inelastic critical stressFcr=(0.658Fy/Fe)Fy
AISC 360-16 Eq. E3-2, for KL/r≤4.71E/Fy. Approaches Fy
Elastic critical stressFcr=0.877Fe
AISC 360-16 Eq. E3-3, for slender columns above the transition. The 0.877 covers initial out-of-straightness.
Nominal compressive strengthPn=FcrAg
Ag = gross area (in²); Pn in kips. Use gross area — bolt holes do not reduce compression. AISC 360-16 Eq. E3-1.
LRFD design strengthϕcPn,ϕc=0.90
Compare to factored load Pu from ASCE 7-16 LRFD combinations. Require ϕcPn≥Pu.
ASD allowable strengthΩcPn,Ωc=1.67
Compare to service load Pa from ASD combinations. Require Pn/Ωc≥Pa
Equivalent weak-axis length for Table 4-1(KL)eff,y=rx/ryKxLx
Converts a strong-axis effective length to the y-axis basis the table uses, so you enter Table 4-1 with the larger of KyLy and this value.
,
rx=4.35in
) of
Fy=50
ksi steel is pinned top and bottom and braced about both axes only at the ends. The unbraced length is
14ft
each way (
K=1.0
). Find
ϕcPn
and
Pn/Ωc
.
Solution. Both lengths equal, so the smaller r governs: minor axis. KL/ry=(1.0)(14×12)/2.54=168/2.54=66.1.
Branch limit: 4.71E/Fy=4.7129000/50=113. Since 66.1<113, use the inelastic branch.
Fe=π2(29000)/66.12=286200/4373=65.4 ksi.
Fcr=0.658(50/65.4)(50)=0.6580.764(50)=0.726(50)=36.3 ksi.
Pn=FcrAg=36.3(14.4)=523 kips.
LRFD: ϕcPn=0.90(523)=471 kips. ASD: Pn/Ωc=523/1.67=313 kips.
Sanity: Fcr=36.3 ksi is well below Fy=50 ksi (buckling reduced it ~27%), as expected for a moderately slender column; Manual Table 4-1 lists ϕcPn≈471 kips at KL=14ft — a match.
Fcr=0.65850/65.4(50)=36.3ksi
Slender column — elastic branch
Problem. A W8×31 (Ag=9.13in2, ry=2.02in) of Fy=50 ksi steel acts as a pinned strut with an unbraced length of 22ft about its weak axis (K=1.0). Find the LRFD design compressive strength.
•Citing a handbook page for column strength. The PE Civil Handbook §4.2 has no member-strength tables; compression design is AISC 360-16 Ch E. Cite the code, not a handbook page.
•Putting the strength on the wrong branch: KL/r≤4.71E/Fy is inelastic (0.658 form); above it is elastic (0.877Fe). Memorize the limit values 113 (Fy=50) and 134 (Fy=36).
•Mixing LRFD and ASD: ϕc=0.90 MULTIPLIES Pn; Ωc=1.67 DIVIDES it. Decide the format up front and never compare a factored load against an allowable strength.
•Reducing compression area for bolt holes. Compression uses gross area Ag — the fasteners fill the holes and carry bearing. Net area is a tension concept.
•Wrong code edition: NCEES supplies AISC 360-16 / Manual 15th ed. Do not use AISC 360-22 constants or K tables from another edition.