Module 3: Timber Beams - Theory & Concepts

Module 3: Timber Beams

$Learning Objectives$

Develop a complete NSCP timber-beam workflow from loads through final governing utilization.
Check bending strength using the applicable adjusted bending design value and beam-stability provisions.
Evaluate shear and bearing without overgeneralizing near-support load reductions.
Calculate immediate deflection and recognize long-term deformation and creep effects.
Apply size, repetitive-member, volume, and other factors only within their code-defined product scope.
Coordinate beam depth, bracing, penetrations, supports, moisture, and exposed detailing with architectural requirements.

$NSCP Code Basis$

Use NSCP 2015 Section 616 for member design equations and Section 617 for sawn-lumber values and adjustments, or Section 618 for structural glulam. Connection and notching details must be coordinated with the appropriate Chapter 6 provisions.

$Timber Beam Design Objective$

A review-ready timber beam design must connect the architectural span and framing concept to verified material values, strength and stability checks, support bearing, serviceability, and constructible detailing. The flowchart below is the canonical sequence for completing those checks.

$Beam Design Workflow$

The beam is acceptable only when every applicable strength, stability, support, serviceability, and detailing check passes. Any failed check requires redesign and a complete recheck.

NSCP Timber Beam Design Workflow

Reference-value adjustment, flexure/stability, shear, bearing, serviceability, and detailing sequence for timber beams.

Define span, supports, loads, product, grade, and service conditions → Compute reactions, shear, moment, and deflection demand; Compute reactions, shear, moment, and deflection demand → Obtain verified Fb, Fv, Fc⊥, E, and Emin values for the selected product; Obtain verified Fb, Fv, Fc⊥, E, and Emin values for the selected product → Form property-specific adjusted chains: Fb*, Fv′, Fc⊥′, E′, and Emin′; Form property-specific adjusted chains: Fb*, Fv′, Fc⊥′, E′, and Emin′ → Does bending require beam-stability evaluation?; Does bending require beam-stability evaluation? — Yes → Determine effective unbraced length, RB, FbE, CL, and final Fb′; Does bending require beam-stability evaluation? — No / permitted bracing → Verify permitted bracing and form final Fb′; Determine effective unbraced length, RB, FbE, CL, and final Fb′ → Check bending demand against Fb′; Verify permitted bracing and form final Fb′ → Check bending demand against Fb′; Check bending demand against Fb′ → Check shear using Fv′ and only permitted near-support provisions; Check shear using Fv′ and only permitted near-support provisions → Check support bearing using Fc⊥′ and qualifying Cb if permitted; Check support bearing using Fc⊥′ and qualifying Cb if permitted → Check immediate and long-term deflection; Check immediate and long-term deflection → Check notches, holes, bracing, connections, and exposure; Check notches, holes, bracing, connections, and exposure → Do all required beam checks pass?; Do all required beam checks pass? — Yes → Document governing beam check and factor chain; Do all required beam checks pass? — No → Revise section, span, restraint, support, or detail; Revise section, span, restraint, support, or detail → Compute reactions, shear, moment, and deflection demand

Define span, supports, loads, product, grade, and service conditions: terminator
Compute reactions, shear, moment, and deflection demand: process
Obtain verified Fb, Fv, Fc⊥, E, and Emin values for the selected product: process
Form property-specific adjusted chains: Fb*, Fv′, Fc⊥′, E′, and Emin′: subprocess
Does bending require beam-stability evaluation?: decision
Determine effective unbraced length, RB, FbE, CL, and final Fb′: process
Verify permitted bracing and form final Fb′: process
Check bending demand against Fb′: process
Check shear using Fv′ and only permitted near-support provisions: process
Check support bearing using Fc⊥′ and qualifying Cb if permitted: process
Check immediate and long-term deflection: subprocess
Check notches, holes, bracing, connections, and exposure: subprocess
Do all required beam checks pass?: decision
Revise section, span, restraint, support, or detail: process
Document governing beam check and factor chain: terminator

Rectangular Section Properties

Section modulus and moment of inertia for a solid rectangular beam.

S=\frac{bd^2}{6} \qquad I=\frac{bd^3}{12}

Variables

Symbol	Description	Unit
$b$	Beam width.	-
$d$	Beam depth in the bending direction.	-
$S$	Elastic section modulus.	-
$I$	Second moment of area.	-

Bending Stress

Elastic bending stress at the extreme fiber of a beam.

f_b=\frac{M_{\max}}{S}\le F_b'

Variables

Symbol	Description	Unit
$M_{\max}$	Maximum design bending moment.	-
$S$	Section modulus about the bending axis.	-
$f_b$	Actual bending stress.	-
$F_b'$	Adjusted bending design value including all applicable factors.	-

$Form Every Beam Property on Its Own Adjustment Chain$

A timber beam does not have one universal "adjusted strength." Each limit state uses the property it needs.

For sawn lumber in ASD, the common beam chains are:

F_b^* = F_b C_D C_M C_t C_F C_i C_r

F_b' = F_b^* C_L C_{fu}

F_v' = F_v C_D C_M C_t C_i

F_{c\perp}' = F_{c\perp} C_M C_t C_i C_b

E' = E C_M C_t C_i

E_{min}' = E_{min} C_M C_t C_i C_T.

The factor magnitudes still come from the governing table and actual conditions. $C_F$ is a sawn-lumber size factor; do not replace a glulam/SCL volume or product adjustment with it. $C_b$ is used only when the bearing-area conditions permit it. $C_{fu}$ is relevant only to the permitted flat-use bending case.

$Beam-Stability Inputs Must Come From the Actual Restraint Layout$

Before calculating $R_B$ or $C_L$ :

identify the unsupported length $l_u$ between points that actually restrain the compression edge;
determine the load/support case used by the governing NDS effective-length table;
obtain the corresponding effective beam length $l_e$ rather than substituting the clear span automatically;
verify end restraint against rotation at bearings and any required continuous/discrete lateral support; and
calculate $E_{min}'$ and $F_b^*$ before evaluating $F_{bE}$ and $C_L$ .

The clear span, unsupported length, and effective beam length are different quantities. Using the span directly as $l_e$ can be either unconservative or unnecessarily conservative depending on the actual loading and restraint condition.

$Beam Stability$

A laterally unsupported compression edge can move sideways and twist. The beam-stability factor therefore depends on geometry and lateral support conditions. Decking, blocking, diaphragms, framing intersections, and connection details may provide restraint only when they are actually capable of transferring the required stabilizing forces.

Do not assume a ceiling finish or nonstructural partition provides structural bracing.

For the rectangular-beam stability model used in the worked examples,

R_B=\sqrt{\frac{l_e d}{b^2}}

F_{bE}=\frac{1.20E_{min}'}{R_B^2}

and the beam slenderness ratio must satisfy

R_B\le 50.

Let $R=F_{bE}/F_b^*$ . The corresponding stability factor used in the course examples is

C_L= \frac{1+R}{1.9} - \sqrt{ \left(\frac{1+R}{1.9}\right)^2 - \frac{R}{0.95} }.

Use $C_L$ only where the adopted NSCP timber provision requires it and with the actual effective unbraced length.

$Lateral-Support Decision Guide$

For sawn rectangular members, depth-to-breadth ratio is a useful detailing screen:

Nominal beam proportion	Prescriptive lateral-support alternative
$d/b\le2$	No lateral support required by this prescriptive rule
$2<d/b\le4$	Hold the ends in position with blocking, bridging, hangers, fastening to framing, or another acceptable restraint
$4<d/b\le5$	Hold the compression edge in line continuously and restrain the ends at bearings against rotation/lateral displacement
$5<d/b\le6$	Add bridging/full-depth blocking/diagonal cross-bracing at intervals not exceeding 8 ft, continuously restrain the compression edge, and restrain the ends
$6<d/b\le7$	Hold both edges in line continuously and restrain the ends at bearings

These are the NDS-family prescriptive alternatives for rectangular sawn-lumber bending members. Members outside their scope, or members using the analytical stability method, require the applicable $C_L$ calculation and effective-length provisions rather than extrapolating the table.

$Size-Factor Scope$

Do not apply one generic power-law size-factor equation to every timber beam. Sawn dimension lumber, larger sawn members, glulam, and other engineered products use different code provisions and tables. Determine the product category first, then use the size or volume adjustment specifically permitted for that category.

Rectangular Beam Shear Stress

Maximum elastic shear stress for a solid rectangular section away from code-permitted near-support reductions.

f_v=\frac{3V}{2bd}\le F_v'

Variables

Symbol	Description	Unit
$V$	Design shear at the section being checked.	-
$b$	Beam width.	-
$d$	Beam depth.	-
$f_v$	Actual maximum shear stress for a rectangular section.	-
$F_v'$	Adjusted shear design value.	-

$Loads Near a Support$

NSCP/NDS timber provisions allow specific treatment of loads close to a support because the internal force can be transferred partly by diagonal compression. Do not translate this into the blanket statement that every load within one beam depth may be ignored. Apply the code rule to the actual load type, location, and support geometry.

$Bearing at Supports$

End reactions must enter the support through sufficient bearing area. Check compression perpendicular to grain and ensure the seat length, connector geometry, end distance, and moisture/detailing condition are constructible.

Deep beams often satisfy flexure but require larger support seats than an architectural sketch initially shows.

Simply Supported Beam Deflection Under Uniform Load

Elastic midspan deflection for a prismatic simply supported beam carrying uniform load over the full span.

\Delta_{\max}=\frac{5wL^4}{384EI}

Variables

Symbol	Description	Unit
$w$	Uniform line load.	-
$L$	Span.	-
$E$	Applicable modulus of elasticity for the serviceability calculation.	-
$I$	Second moment of area.	-
$\Delta_{\max}$	Elastic midspan deflection.	-

$Separate Immediate and Time-Dependent Deflection$

Wood members require a serviceability calculation that distinguishes short-term elastic deformation from deformation that grows under sustained load.

A convenient NDS bookkeeping form is

\Delta_T=\Delta_{ST}+K_{cr}\Delta_{LT}

where $\Delta_{ST}$ is the immediate deflection associated with short-term load, $\Delta_{LT}$ is the immediate elastic deflection attributable to the sustained load component, and $K_{cr}$ is the code creep/time-dependent deformation factor for the applicable moisture condition and product.

For ordinary NDS member design, $K_{cr}$ is commonly in the 1.5 to 2.0 range depending on service moisture. Do not apply one multiplier to the entire service-load deflection. Identify which portion of the load is sustained and compare the resulting total and component deflections with the actual project/occupancy criteria.

$Serviceability and Long-Term Deformation$

Strength alone does not ensure a successful timber floor or roof. Check the serviceability limits applicable to the occupancy, finishes, partitions, glazing, drainage, and structural system. Wood is time-dependent, so sustained loading and moisture can increase long-term deformation beyond the immediate elastic value.

Use the code-prescribed time-effect/creep treatment for the product and loading. Do not present a single span ratio as universally applicable to every architectural condition.

$Interactive Exploration$

Move the section-position slider from one support to the other: shear changes sign at midspan, moment peaks there, and deflection returns to zero at both supports. The elevation uses the analytical uniform-load deflection curve and its stated multiplier; the force diagrams use normalized ordinates. Increase depth while holding the load fixed to compare its squared effect on bending resistance with its cubed effect on stiffness. Reset restores the starting beam.

Controls

100 mm

300 mm

5000 mm

4.00 kN/m

12.0 MPa

1.2 MPa

9000 MPa

50 %

Elevation · physical geometry + labeled deflection exaggeration

Cross-section · physical scale

Maximum moment12.50 kN·m

Maximum shear10.00 kN

Bending stress8.33 MPa

Shear stress0.50 MPa

Elastic deflection16.08 mm

Span / deflectionL/311

Bending OK · 69%Shear OK · 42%

Internal-force diagrams · full-span uniform load

Shear at x = 2500 mm0.00 kN

Moment at selected section12.50 kN·m

Deflection at selected section16.08 mm

Scope: simply supported solid rectangular member, full-span uniform load, immediate elastic deflection, and user-supplied adjusted design values. The dashed deflected shape is explicitly exaggerated; beam stability, bearing, creep, notches/holes, connections, and load combinations remain separate checks.

$Prescriptive Sawn-Lumber Notch Limits$

For solid sawn-lumber bending members within the NDS prescriptive notch provisions:

an end notch must not exceed one-fourth of the member depth;
an interior notch must not exceed one-sixth of the member depth;
an interior notch length must not exceed one-third of the member depth;
interior notches are not permitted in the middle third of the span; and
for members at least 4 in. nominal thickness, a notch on the tension side is not permitted except at the member end.

These limits do not authorize holes or cuts in glulam, LVL/SCL, I-joists, CLT, or proprietary engineered products. Those products require their own code/manufacturer provisions. Passing a geometry limit also does not waive the required reduced-section, shear, splitting, and tension-perpendicular-to-grain checks.

$Notches, Holes, and Penetrations$

Notches and holes disturb stress flow and can create tension perpendicular to grain or severe shear concentrations. Never locate penetrations solely from an MEP coordination drawing. Verify that the member type and code provisions permit the opening and that the remaining section and connection zone remain adequate.

For exposed beams, early MEP coordination can avoid field drilling that invalidates the original design.

Use this quantitative workflow for every proposed cut:

classify it as an end notch, interior notch, tapered cut, bored hole, or connection hole;
locate it relative to supports, peak shear, and peak moment;
verify the applicable NSCP geometry limit before assuming the cut is permitted;
recalculate the reduced section and local shear/bending demand where required;
check splitting and tension perpendicular to grain; and
move the service or provide engineered reinforcement when the prescriptive geometry is exceeded.

Near a support, do not automatically reduce shear because a load is close to the reaction. Any permitted near-support treatment depends on the actual load location, bearing arrangement, and governing timber provision.

For a permitted rectangular solid-sawn end notch on the tension face, the NDS-family notch treatment used by the NSCP timber provisions includes the squared remaining-depth ratio. With original depth $d$ , remaining depth $d_n$ , width $b$ , and adjusted shear value $F_v'$ , the corresponding shear-resistance form is

$V_r'=\frac{2}{3}F_v'bd_n\left(\frac{d_n}{d}\right)^2.$

The squared ratio is essential: using only one power of $d_n/d$ overstates the resistance. This equation is not a general opening rule and must not be transferred to interior notches, engineered-wood products, or configurations outside the provision's scope.

$Complete Timber-Beam Solution Checklist$

A review-ready solution should explicitly show the adjusted bending value and any $C_L$ reduction, bending utilization, shear utilization, support bearing, immediate deflection, long-term/creep-sensitive deflection where relevant, lateral-restraint assumptions, and notch/hole/connection checks.

$Architectural Design Implications$

Increasing beam depth is usually far more efficient structurally than increasing width because $S$ varies with $d^2$ and $I$ with $d^3$ . That same depth affects floor-to-floor height, ceiling zones, daylight, façade heads, duct routes, and visual proportion.

A shallower architectural profile may require closer spacing, stronger material, glulam/LVL, composite action, additional supports, or a different structural system rather than simply accepting higher stress.

Key Takeaways

Timber beam design is a coordinated check of bending, stability, shear, bearing, and serviceability.
The core elastic deflection equation must be present and used with consistent units and appropriate serviceability properties.
Size and volume effects are product-specific; do not apply one generic factor to every wood beam.
Near-support shear provisions have conditions and are not permission to ignore all loads within one beam depth.
Beam depth, bracing, support seats, penetrations, creep, moisture, and architectural coordination should be resolved together.

$References$

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 timber bending, shear, bearing, beam stability, serviceability, and related detailing; consult the official licensed code for complete provisions and applicability limits.

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