Module 8: Steel Beams and Flexural Members

Module 8: Steel Beams and Flexural Members

$Learning Objectives$

Classify flexural elements and identify the applicable NSCP Section 506 limit states.
Evaluate yielding, local buckling, and lateral-torsional buckling without assuming plastic moment capacity always governs.
Check beam shear using NSCP Section 507 and recognize when web slenderness or openings require additional treatment.
Evaluate deflection and other serviceability considerations under Section 512.
Recognize combined axial force and bending under Section 508.
Relate beam depth, unbraced length, bracing, floor vibration, penetrations, and fire protection to architectural design.

$NSCP Code Basis$

Use NSCP Section 506 — Flexure, Section 507 — Shear, Section 508 — Combined Forces and Torsion, and Section 512 — Serviceability Design Considerations. The applicable flexural subsection depends on section shape, symmetry, compactness, bending axis, and web/flange slenderness.

$Steel Beam Design Objective$

A review-ready steel beam design must select the correct NSCP flexural case, evaluate stability and shear, satisfy project serviceability demands, and coordinate bracing, connections, penetrations, fire protection, and architectural depth. The flowchart below is the canonical sequence.

$Beam Response Diagrams$

Use the physical load/support sketch first, then move the section location x/L probe along the span. The same selected section reports dimensional shear, bending moment, and elastic deflection while the three diagram shapes remain normalized for readable comparison. Change $E$ or $I_x$ to see deflection change without falsely changing the force diagrams, then use Reset to restore the reference case.

Controls

8.00 m

12 kN/m

200000 MPa

300 10⁶ mm⁴

0.50

Maximum support shear48.0 kN

Maximum midspan moment96.0 kN·m

Maximum midspan deflection10.67 mm

Probe location x4.00 m

Probe shear V(x)0.0 kN

Probe moment M(x)96.0 kN·m

Probe deflection δ(x)10.67 mm downward

Scope: prismatic simply supported beam, full-span uniform load, linear-elastic deflection, constant E and Ix. The response diagrams use normalized ordinates only for visual comparison; the numerical probe values are dimensional. Serviceability criteria, LTB, local buckling, shear strength, vibration, composite action, and connection flexibility require separate checks.

$Steel Beam Design Workflow$

The correct flexural equation is selected only after the section shape, bending axis, symmetry, element classification, and bracing condition are known. The workflow therefore branches before the strength equation is chosen.

Steel Beam Case-Selection and Design Workflow

Section-shape, axis, local-buckling, LTB, shear, serviceability, and interaction sequence for NSCP steel flexural members.

Define loads, bracing, section, axis, and required strength → Classify flange/web elements for the actual flexural case; Classify flange/web elements for the actual flexural case → Which Section 506 flexural case applies?; Which Section 506 flexural case applies? — F2-type case → Compact doubly symmetric I-shape major-axis path: yielding + LTB; Which Section 506 flexural case applies? — Other case → Select applicable F3–F12 path by shape, axis, symmetry, and element slenderness; Compact doubly symmetric I-shape major-axis path: yielding + LTB → Does the selected case require LTB evaluation?; Select applicable F3–F12 path by shape, axis, symmetry, and element slenderness → Does the selected case require LTB evaluation?; Does the selected case require LTB evaluation? — Yes → Determine Lb, Lp/Lr where applicable, Cb, and governing LTB strength; Does the selected case require LTB evaluation? — No → Evaluate applicable flange/web local-buckling reduction; Determine Lb, Lp/Lr where applicable, Cb, and governing LTB strength → Evaluate applicable flange/web local-buckling reduction; Evaluate applicable flange/web local-buckling reduction → Select web-shear case, Cv, and stiffening requirements; Select web-shear case, Cv, and stiffening requirements → Check deflection, vibration, drainage, and finishes; Check deflection, vibration, drainage, and finishes → Significant axial force or torsion?; Significant axial force or torsion? — Yes → Apply required combined-force or torsion interaction; Significant axial force or torsion? — No → Verify bracing, connections, penetrations, fire, and coordination; Apply required combined-force or torsion interaction → Verify bracing, connections, penetrations, fire, and coordination; Verify bracing, connections, penetrations, fire, and coordination → Do all required beam checks pass?; Do all required beam checks pass? — Yes → Document governing beam limit state; Do all required beam checks pass? — No → Revise section, bracing, span, framing direction, or opening/detail; Revise section, bracing, span, framing direction, or opening/detail → Classify flange/web elements for the actual flexural case

Define loads, bracing, section, axis, and required strength: terminator
Classify flange/web elements for the actual flexural case: subprocess
Which Section 506 flexural case applies?: decision
Compact doubly symmetric I-shape major-axis path: yielding + LTB: process
Select applicable F3–F12 path by shape, axis, symmetry, and element slenderness: subprocess
Does the selected case require LTB evaluation?: decision
Determine Lb, Lp/Lr where applicable, Cb, and governing LTB strength: subprocess
Evaluate applicable flange/web local-buckling reduction: process
Select web-shear case, Cv, and stiffening requirements: subprocess
Check deflection, vibration, drainage, and finishes: process
Significant axial force or torsion?: decision
Apply required combined-force or torsion interaction: process
Verify bracing, connections, penetrations, fire, and coordination: process
Do all required beam checks pass?: decision
Revise section, bracing, span, framing direction, or opening/detail: process
Document governing beam limit state: terminator

$Section 506 Flexural Case Selection$

The compact doubly symmetric I-shape equations are only one path through the flexural chapter. Use the case that matches the actual member.

Member/behavior family	AISC 14th Edition / ANSI/AISC 360-10 flexural path corresponding to NSCP 2015
Compact doubly symmetric I-shape / channel, major-axis bending	F2-type yielding and LTB checks
Doubly symmetric I-shape with noncompact/slender flange	F3-type local-flange-buckling plus LTB/yielding
Other I-shape cases with noncompact/slender webs	F4/F5-type provisions as applicable
I-shape / channel, minor-axis bending	F6-type path
Square/rectangular HSS and box sections	F7-type path
Round HSS	F8-type path
Tees and double angles	F9-type path
Single angles	F10-type path
Rectangular bars and rounds	F11-type path
Unsymmetrical shapes not covered by the preceding cases	F12-type path

The table is a navigation map. Verify the exact scope, symmetry, compactness, and loading conditions in the adopted NSCP/AISC provision before using its equations.

Plastic Moment

Plastic moment is an upper flexural benchmark for sections and bracing conditions that permit full plastic behavior; it is not automatically the design strength of every beam.

M_p=F_yZ_x

Variables

Symbol	Description	Unit
$F_y$	Specified yield strength.	-
$Z_x$	Plastic section modulus about the bending axis.	-
$M_p$	Plastic moment.	-

$Plastic Moment Is Conditional$

A steel beam is not simply "designed based on plastic moment." Noncompact or slender elements, long unbraced lengths, other section shapes, holes, and different loading/support conditions can reduce nominal flexural strength below $M_p$ .

$Lateral-Torsional Buckling$

When the compression flange lacks adequate lateral restraint, the beam can move laterally and twist. The nominal strength therefore depends on unbraced length and the applicable Section 506 case.

For common compact doubly symmetric I-shapes, $L_p$ and $L_r$ separate full-plastic, inelastic LTB, and elastic LTB ranges. Moment gradient can be represented by $C_b$ where the provision permits it.

$LTB Reference Equations for Compact Doubly Symmetric I-Shapes$

For the common NSCP/AISC F2-style case used by the course simulator, first establish the limiting unbraced lengths:

L_p=1.76r_y\sqrt{\frac{E}{F_y}}

L_r= 1.95r_{ts}\frac{E}{0.7F_y} \sqrt{ \frac{Jc}{S_xh_o} + \sqrt{ \left(\frac{Jc}{S_xh_o}\right)^2 + 6.76\left(\frac{0.7F_y}{E}\right)^2 } }

with $c=1.0$ for the doubly symmetric I-shape case. Then classify the unbraced segment:

Range	Governing major-axis behavior
$L_b\le L_p$	Full plastic-moment range where the other F2 conditions are satisfied
$L_p<L_b\le L_r$	Inelastic lateral-torsional buckling
$L_b>L_r$	Elastic lateral-torsional buckling

For the inelastic range,

M_n= C_b\left[ M_p-(M_p-0.7F_yS_x) \frac{L_b-L_p}{L_r-L_p} \right] \le M_p.

For $L_b>L_r$ in the same compact doubly symmetric I-shape case,

F_{cr}= \frac{C_b\pi^2E}{(L_b/r_{ts})^2} \sqrt{ 1+0.078\frac{Jc}{S_xh_o} \left(\frac{L_b}{r_{ts}}\right)^2 }

and

M_n=F_{cr}S_x\le M_p.

These equations belong only to the stated F2-type case. Other section shapes, bending axes, and local-slenderness conditions require their own Section 506 path.

Moment-Gradient Factor Cb

Quarter-point moment expression for applicable singly symmetric single-curvature and doubly symmetric unbraced segments.

C_b= \frac{12.5M_{max}} {2.5M_{max}+3M_A+4M_B+3M_C}

Variables

Symbol	Description	Unit
$M_{max}$	Maximum absolute moment in the unbraced segment.	-
$M_A$	Absolute moment at the quarter point.	-
$M_B$	Absolute moment at mid-length.	-
$M_C$	Absolute moment at the three-quarter point.	-

$Cb Is Not an Arbitrary Bonus$

Use $C_b=1.0$ when a larger permitted value has not been established from the actual moment diagram. Do not increase $C_b$ merely to obtain a passing beam.

$Interactive Exploration$

Move the unbraced length through $L_p$ and $L_r$ and compare the selected $M_n$ with $M_p$ . Then increase $C_b$ above the uniform-moment baseline of 1.0 to see how a permitted favorable moment gradient can raise the modeled strength, subject to the $M_p$ cap. $L_p$ and $L_r$ identify equation ranges and do not guarantee an immediate strength drop when $C_b>1$ . Use Reset to return to $C_b=1.0$ .

Controls

10.00 ft

0.80

0.60

0.40

Lp5.47 ft

Lr14.35 ft

Plastic moment Mp277.1 kip-ft

Behavior regioninelastic LTB range

Moment-gradient factor1.47

Nominal moment Mn277.1 kip-ft

The section properties are a fixed representative compact doubly symmetric I-shape so the graph isolates Lb and the moment pattern. Cb is derived from the three normalized quarter-point moment magnitudes rather than selected directly. Lp and Lr identify equation ranges; when the calculated Cb is above 1.0, Mn can remain capped at Mp for part of an LTB range. Project design must use the actual section properties and applicable NSCP Section 506 case, including local buckling, loading position, bracing adequacy, and applicable limits on Cb.

$Bracing Is a Structural System$

A deck, slab, joist, purlin, cross-frame, or discrete brace should be credited only when its attachment and stiffness can actually restrain the required beam movement. An architectural ceiling or light partition is not automatically a lateral brace.

Reducing unbraced length can sometimes improve beam capacity more efficiently than increasing steel tonnage.

$Flexural Available Strength$

After the correct Section 506 nominal moment $M_n$ is obtained for the selected case, the ordinary Chapter F available strength uses

M_c=0.90M_n \quad \text{(LRFD)}

M_c=\frac{M_n}{1.67} \quad \text{(ASD)}

unless the governing provision explicitly specifies otherwise. Apply the factor to the governing nominal flexural strength after all applicable yielding, LTB, and local-buckling checks.

$Shear$

Steel beam shear is resisted primarily by the web in common I-shaped members, but the actual stress field is not literally uniform over the web. Code design uses idealized strength models that depend on web proportions, material strength, stiffeners, and, for slender webs, buckling/tension-field behavior.

Web openings for ducts or architectural services interrupt this force path and require explicit evaluation.

$Shear Case Selection$

Before taking $C_v=1.0$ , classify the web and the shear-panel configuration.

determine the clear web depth and thickness using the definition required by the selected provision;
compare the web slenderness with the applicable shear limits;
determine whether transverse stiffeners are required or intentionally provided;
establish whether the member is a rolled shape, built-up girder, or other case with additional provisions;
check openings, copes, concentrated forces, and connection regions separately where they disturb the web force path; and
use tension-field action only when the complete panel/stiffener/flange conditions permit it.

A beam can pass flexure and still require redesign for web shear, web instability, concentrated-force effects, or an opening.

$Beam-Shear Calculation Framework$

For a rolled I-shape or channel web in the basic Section 507/AISC G2 framework,

V_n=0.6F_yA_wC_v

where $A_w$ is the web shear area and $C_v$ depends on web slenderness and stiffening. A compact/non-slender web may have $C_v=1.0$ ; slender webs require the applicable buckling reduction and, for plate girders, potentially transverse-stiffener/tension-field provisions.

Do not use $C_v=1.0$ simply because the example did so. Check $h/t_w$ and the governing shear case first.

For the other singly or doubly symmetric web/channel cases covered by the AISC 360-10 G2 framework, determine $C_v$ from web slenderness:

C_v=1.0 \qquad \text{when } \frac{h}{t_w}\le1.10\sqrt{\frac{k_vE}{F_y}},

C_v= \frac{1.10\sqrt{k_vE/F_y}}{h/t_w} \qquad \text{when } 1.10\sqrt{\frac{k_vE}{F_y}} < \frac{h}{t_w} \le 1.37\sqrt{\frac{k_vE}{F_y}},

and

C_v= \frac{1.51Ek_v}{(h/t_w)^2F_y} \qquad \text{when } \frac{h}{t_w}> 1.37\sqrt{\frac{k_vE}{F_y}}.

For an unstiffened web within the applicable range, $k_v=5.0$ except for the tee-stem case, which uses its own provision. Stiffened webs require the panel aspect ratio and transverse-stiffener rules before $k_v$ is selected. Tension-field action is a separate post-buckling design path and must not be assumed automatically.

$Shear Available Strength Is Case-Specific$

Under the AISC 14th Edition / ANSI/AISC 360-10 Chapter G framework adapted by NSCP 2015, most shear provisions use $\phi_v=0.90$ for LRFD and $\Omega_v=1.67$ for ASD. The special $\phi_v=1.00$ and $\Omega_v=1.50$ values apply to the web of a rolled I-shaped member satisfying

\frac{h}{t_w}\le2.24\sqrt{\frac{E}{F_y}},

for the applicable web-shear direction. Do not extend that special resistance factor to channels or other shapes merely because their web also has $C_v=1.0$ .

Therefore, determine the shear case first, then apply its resistance/safety factor. Do not assume the special $1.00/1.50$ factors apply to every web, HSS, angle, tee, weak-axis shear case, or plate girder.

$Serviceability$

Section 512 requires serviceability to be evaluated for the structure and occupancy. Deflection limits such as $L/360$ or $L/240$ are common project criteria in certain applications, but they are not universal values for every steel beam.

Review total deflection, live-load deflection, ponding or drainage, vibration, façade/partition sensitivity, camber, connection slip, and other project-specific performance requirements.

$Serviceability Selection Table$

Deflection limits are project/occupancy criteria rather than one universal steel-beam number. Use the governing building code and project criteria, but keep these common project/reference criteria distinct:

Check	Common project/reference criterion	What to verify
Live-load floor/roof deflection	values such as $L/360$ may be specified	Ceiling, partition, façade, finish sensitivity
Total-load deflection	values such as $L/240$ may be specified	Drainage, cladding, architectural alignment
Cantilever deflection	usually project-specific	Edge glazing, canopy drainage, façade tolerances
Vibration	not controlled by a simple $L/n$ limit	Frequency, acceleration, occupancy sensitivity

The course should state the criterion used in each example rather than presenting $L/360$ or $L/240$ as an automatic NSCP limit for every member.

$Combined Axial Force and Bending$

Columns in moment frames, transfer elements, roof members, and inclined members may experience substantial axial force together with bending. Use NSCP Section 508 / AISC 360-10 H1 interaction rather than checking axial and flexural strengths independently.

For the H1-1 form used by the course interaction simulator, define $P_r$ as the required axial strength, $P_c$ as the available axial strength on the selected LRFD/ASD basis, and $M_{rx},M_{ry}$ and $M_{cx},M_{cy}$ as required and available moments on that same design basis.

When

\frac{P_r}{P_c}\ge0.20,

check

\frac{P_r}{P_c} + \frac{8}{9} \left( \frac{M_{rx}}{M_{cx}}+ \frac{M_{ry}}{M_{cy}} \right) \le1.0.

When

\frac{P_r}{P_c}<0.20,

check

\frac{P_r}{2P_c} + \frac{M_{rx}}{M_{cx}}+ \frac{M_{ry}}{M_{cy}} \le1.0.

Required moments must already include the second-order effects demanded by the adopted stability analysis. Verify that the member symmetry and loading fall within the scope of this H1 path; unsymmetric/special cases require the applicable Section 508 provision.

$Interactive Exploration$

Move the normalized axial and flexural demand point relative to the modeled Section 508/H1-style boundary. Watch the equation branch change at $P_u/P_c=0.20$ , compare the selected moment ratio with the boundary value at the same axial ratio, and use the interaction value as the governing acceptance metric. Required second-order effects must already be included in demand.

Controls

0.40

0.45

Pu/Pc0.400

Mr/Mc0.450

Boundary Mr/Mc at selected Pu/Pc0.675

Moment-ratio margin0.225

Interaction value0.800

Inside modeled interaction limit

This is a normalized uniaxial interaction visual after required second-order effects are included in demand. A point inside this envelope only satisfies the modeled interaction expression; it is not a complete member approval. Biaxial bending, torsion, member-specific strength calculations, stability, and alternative Section 508 cases require their applicable equations.

$Architectural Beam Decisions$

Beam depth competes directly with ceiling height, façade heads, ducts, lighting, and vertical circulation. A shallower section may require more weight, closer supports, composite action, a different framing direction, or deeper local transfer members.

For exposed steel, also coordinate flange/web proportions, connection plates, stiffeners, bolt heads, weld finish, drainage, corrosion protection, and fireproofing. "Clean" architectural steel requires more detailing, not less.

Key Takeaways

NSCP Section 506 flexural strength depends on section shape, compactness, bending axis, and lateral bracing; $M_p$ is not universally available.
Lateral-torsional buckling can govern otherwise strong beams and is strongly influenced by unbraced length.
Shear and serviceability require separate checks under Sections 507 and 512.
Deflection criteria are application-specific; do not present one span ratio as a universal code limit.
Combined axial force and bending require Section 508 interaction checks, and architectural beam depth must be coordinated with building systems.

$References$

Association of Structural Engineers of the Philippines (ASEP) — National Structural Code of the Philippines, C101-15, Volume I, Seventh Edition (2015) — Governing course reference for Sections 506–508 and 512 covering flexure, shear, combined forces/torsion, and serviceability; consult the official licensed code for complete equations, applicability limits, exceptions, and detailing requirements.
AISC — Historic Standards and Steel Construction Manuals — NSCP 2015 Chapter 5 adapts the AISC 14th Edition framework based on ANSI/AISC 360-10. Use the adopted NSCP text as governing and the corresponding historical AISC edition only as a technical cross-reference.