TrussCalc

NDS-2024 sawn lumber roof truss analysis — 2025 CBC / ASCE 7-22

Unbalanced snow load per ASCE 7-22 §7.6 not checked — verify with jurisdiction before submitting.
Applies to: Roof Truss T1 — main span
CALC
Project
1550 Bluebird Lane, La Jolla, CA 92037
Job Ref.
 
Section
Roof Truss T1 — main span
Sheet no./rev.
1 of 1 / 1
Calc. by
 
Date
Chk'd by
 
Date
 
App'd by
 
Date
 
Roof Truss Design Calculations
Sawn lumber pin-jointed roof truss checked to NDS-2024 Allowable Stress Design (2025 CBC / ASCE 7-22) — truss 1 of 1: Roof Truss T1 — main span
Design basis & codes
Governing code2025 CBC / 2024 IBC
Material standardANSI/AWC NDS-2024 — National Design Specification for Wood Construction
Reference design valuesNDS Supplement 2024, Table 4A — visually graded dimension lumber
LoadsASCE 7-22 / IBC Ch. 16 — D, Lr/S applied at panel points
Design methodAllowable Stress Design (ASD), pin-jointed planar analysis
Truss configuration & geometry
Truss typeFink (W) truss
Overall span (heel to heel)L = 28.00 ft
Roof pitch5.0 : 12  (θ = 22.6°)
Apex rise above bearingH = 5.83 ft
Rafter length (heel to apex)Lr = 15.17 ft
Eave overhang (each side)Loh = 2.00 ft horizontal (2.17 ft along the rafter tail), both sides
Overall roof widthL + 2 Loh = 32.00 ft
Truss spacings = 24 in o.c.
Heel bearing length providedLb = 3.50 in
Joints / members7 joints, 11 members — statically determinate (m + 3 = 2j)
Member sizes & material
Species / gradeDF-L No.2
Top chord2x6 — A = 8.25 in², S = 7.56 in³
Bottom chord2x6 — A = 8.25 in², S = 7.56 in³
Webs2x4 — A = 5.25 in²
Out-of-plane restraintChords continuously braced by sheathing / ceiling; compression webs laterally braced at mid-length
BendingFb = 900 psi
Tension parallel to grainFt = 575 psi
Compression parallel to grainFc = 1,350 psi
Compression perpendicular to grainFc⊥ = 625 psi
Modulus of elasticityE = 1.60 × 10⁶ psi, Emin = 0.58 × 10⁶ psi
Load duration factorCD = 1.15
Repetitive member factor (NDS 4.3.9)Cr = 1.15 — members spaced 24″ o.c. ≤ 24″
Wet service / temperature / incisingCM = Ct = Ci = 1.00 (dry, normal temperature, un-incised)
Applied loading
Load conditionRoof — snow load (S), C_D = 1.15
Roof dead loadDroof = 15 psf (horizontal projection)
Roof live / snow loadLr or S = 30 psf
Ceiling / bottom chord dead loadDclg = 10 psf
Tributary widtht = s / 12 = 2.000 ft
Roof line load (dead)wD = Droof × t = 30.0 lb/ft
Roof line load (live)wL = Lr × t = 60.0 lb/ft
Ceiling line loadwclg = Dclg × t = 20.0 lb/ft
Truss self weight (all members)Wsw = 154 lb — lumped at joints
Total load on trussW = 3,594 lb
Support reactions (left / right)RL = 1,797 lb, RR = 1,797 lb
Reaction componentsRD = 837 lb, RL = 960 lb
Analysis — method of joints
IdealisationFrictionless pin joints, loads applied at panel points, members carry axial force only
SolutionJoint equilibrium ΣFx = ΣFy = 0 solved simultaneously at all 7 joints
OH 2.00 ftOH 2.00 ft3.1kC2.7kC2.7kC3.1kC2.8kT1.9kT2.8kT622C894T894T622CABCDEFGR = 1,797 lbR = 1,797 lbSpan L = 28.00 ft | Rise = 5.83 ft | Pitch 5.0:12Heavy solid = compression (C) · dashed = tension (T) · arrows = panel point loads
Click any member in the diagram to see its governing axial, buckling and deflection results.
Sign conventionT = tension (positive), C = compression (negative)
MemberGroupLengthDead (D)Live (Lr/S)Design (D+Lr)
ABTop chord7.58 ft1,449 C1,638 C3,087 C
BCTop chord7.58 ft1,302 C1,365 C2,667 C
CDTop chord7.58 ft1,302 C1,365 C2,667 C
DETop chord7.58 ft1,449 C1,638 C3,087 C
AFBottom chord9.33 ft1,338 T1,512 T2,850 T
FGBottom chord9.33 ft895 T1,008 T1,903 T
GEBottom chord9.33 ft1,338 T1,512 T2,850 T
BFWeb3.74 ft219 C403 C622 C
FCWeb7.47 ft491 T403 T894 T
CGWeb7.47 ft491 T403 T894 T
GDWeb3.74 ft219 C403 C622 C
Top chord — axial compression (NDS 3.7)
Governing member / lengthDE, L = 7.58 ft
Section / area2x6, A = 8.25 in²
Axial compressionPTC = 3,087 lb
Applied stressfc = P / A = 374.2 psi
Slenderness (strong / weak)le/d = 16.5, le/b = 0.0 — governing 16.5
Reference compression (adjusted, no C_P)Fc* = Fc × CD × CF = 1,708 psi
Critical buckling stressFcE = 0.822 Emin' / (le/d)² = 1,742 psi
Column stability factor (NDS 3.7.1, c = 0.8)CP = 0.698
Allowable compressionFc' = Fc* × CP = 1,192 psi
Utilisationfc / Fc' = 0.314
PASS — Allowable compression exceeds applied compression
Top chord — combined bending plus axial (NDS 3.9.2)
Sheathing / purlin load normal to chordw⊥ = 78.5 lb/ft
Panel length between jointslp = 7.58 ft
Local bending momentM = w⊥ lp² / 8 = 565 lb-ft
Bending stressfb = M × 12 / S = 896 psi
Allowable bendingFb' = Fb × CD × CF × Cr = 1,547 psi
Euler stress about bending axisFcE1 = 1,742 psi
Interaction(fc/Fc')² + fb / [Fb'(1 − fc/FcE1)] = 0.836
PASS — Combined bending and axial interaction is within unity
Bottom chord — axial tension (NDS 3.8)
Governing member / lengthAF, L = 9.33 ft
Axial tensionT = 2,850 lb
Heel joint connection assumedMetal connector plate (Aₙ = 0.85 Ag)
Net section areaAn = 0.85 × Ag = 0.85 × 8.25 = 7.01 in²
Tension stress on net sectionft = T / An = 406.4 psi
Allowable tensionFt' = Ft × CD × CF = 860 psi
Utilisationft / Ft' = 0.473
PASS — Allowable tension exceeds applied tension
Bottom chord — combined tension plus bending (NDS 3.9.1)
Ceiling load on chordw = 22.0 lb/ft
Local bending momentM = w lp² / 8, lp = 9.33 ft = 240 lb-ft
Bending stressfb = 380 psi
Allowable bendingFb' = 1,547 psi
Interactionft/Ft' + fb/Fb' = 0.719
PASS — Combined tension and bending interaction is within unity
Web members — compression buckling
Governing member / lengthBF, L = 3.74 ft
Section / area2x4, A = 5.25 in²
Axial compressionPw = 622 lb
Applied stressfc = P / A = 118.5 psi
Slenderness (strong / weak)le/d = 12.8, le/b = 14.9 — governing 14.9
Reference compression (adjusted, no C_P)Fc* = Fc × CD × CF = 1,785 psi
Critical buckling stressFcE = 0.822 Emin' / (le/d)² = 2,136 psi
Column stability factor (NDS 3.7.1, c = 0.8)CP = 0.749
Allowable compressionFc' = Fc* × CP = 1,337 psi
Utilisationfc / Fc' = 0.089
PASS — Compression webs are adequate for buckling
Web members — tension
Governing memberCG, T = 894 lb
Tension stressft = 170.3 psi
Allowable tensionFt' = 992 psi
Utilisationft / Ft' = 0.172
PASS — Allowable tension exceeds applied tension in webs
Eave overhang — cantilevered rafter tail (both sides)
Tail lengthLoh = 2.00 ft horizontal = 2.17 ft sloped
Tail load normal to rafterw⊥ = 78.5 lb/ft
Cantilever moment at heelM = w⊥ Loh² / 2 = 184 lb-ft
Bending stress in tailfb = M × 12 / S = 293 psi
Allowable bendingFb' = 1,547 psi
Utilisationfb / Fb' = 0.189
Tail load carried to each heelPD = 64 lb, PL = 120 lb — added to the bearing reaction
PASS — Overhang tail bending is within allowable
Heel bearing — compression perpendicular to grain (NDS 3.10)
Reaction at heelR = 1,797 lb
Bearing areaAb = b × Lb = 1.50 × 3.50 = 5.25 in²
Bearing stressfc⊥ = R / Ab = 342.3 psi
Bearing area factorCb = (Lb + 0.375) / Lb = 1.107
Allowable bearingFc⊥' = Fc⊥ × Cb = 692 psi
Utilisationfc⊥ / Fc⊥' = 0.495
PASS — Allowable bearing exceeds applied bearing stress
Deflection — virtual work (unit load method)
Methodδ = Σ (n · N · L) / (A · E) over all 11 members
Controlling jointJoint G at x = 18.67 ft on the bottom chord
Live deflection limitδlim,L = L / 360 = 0.933 in
Live load deflectionδL = 0.097 in
Utilisation (live)δL / δlim,L = 0.104
PASS — Live deflection is less than design deflection
Total deflection limitδlim,T = L / 240 = 1.400 in
Dead load deflectionδD = 0.089 in
Creep factor (NDS App. F, seasoned sawn lumber)Kcr = 1.50
Total load deflection incl. creepδT = δL + Kcr × δD = 0.097 + 1.50 × 0.089 = 0.231 in
Utilisation (total)δT / δlim,T = 0.165
PASS — Total deflection is less than design deflection
Joint connections — NDS Ch. 12 / TPI 1
Connector systemMetal connector plate, 20 ga (0.036 in)
Design value per unitZ' (CD = 1.15, G = 0.50) = 110 lb/in²
Joint zone assumed along each member12 in
JointTypeMemberForce (lb)T/CA req (in²)A avail (in²)D/CResult
AHeelAB3,087C28.0766.00.425PASS
AF2,850T25.9166.00.393PASS
BPanel pointAB3,087C28.0766.00.425PASS
BC2,667C24.2466.00.367PASS
BF622C5.6542.00.135PASS
CApexBC2,667C24.2466.00.367PASS
CD2,667C24.2466.00.367PASS
FC894T8.1342.00.194PASS
CG894T8.1342.00.194PASS
DPanel pointCD2,667C24.2466.00.367PASS
DE3,087C28.0766.00.425PASS
GD622C5.6542.00.135PASS
EHeelDE3,087C28.0766.00.425PASS
GE2,850T25.9166.00.393PASS
FPanel pointAF2,850T25.9166.00.393PASS
FG1,903T17.3066.00.262PASS
BF622C5.6542.00.135PASS
FC894T8.1342.00.194PASS
GPanel pointFG1,903T17.3066.00.262PASS
GE2,850T25.9166.00.393PASS
CG894T8.1342.00.194PASS
GD622C5.6542.00.135PASS
Governing joint utilisationmax (req / avail) = 0.425
PASS — Selected connector fits the required capacity at every joint
  • Plate tooth value 110 psi of gross contact area per TPI 1; plates on both faces.
  • Contact area available assumes a 12 in joint zone along each member.
  • Plate steel net section and lateral resistance in the direction of the load must be confirmed with the plate manufacturer's ESR.
Governing checks summary
CheckDemandCapacityD/CResult
Top chord compression374 psi1,192 psi0.314PASS
Top chord combined (3.9.2)0.8361.0000.836PASS
Bottom chord tension406 psi860 psi0.473PASS
Bottom chord combined (3.9.1)0.7191.0000.719PASS
Web compression118 psi1,337 psi0.089PASS
Web tension170 psi992 psi0.172PASS
Heel bearing, Fc⊥342 psi692 psi0.495PASS
Overhang tail bending293 psi1,547 psi0.189PASS
Joint connections0.4251.0000.425PASS
Deflection (live)0.097 in0.933 in0.104PASS
Deflection (total)0.231 in1.400 in0.165PASS
Result
Truss adequate — all checks pass
Fink (W) truss — L = 28.00 ft, 5.0:12 @ 24″ o.c., TC 2x6 / BC 2x6 / web 2x4 DF-L No.2 — governing D/C = 0.836
Notes & limitations
  1. Planar pin-jointed analysis; joint fixity and chord continuity are neglected, which is conservative for axial force and unconservative for joint moments.
  2. Top chord is assumed continuously braced laterally by roof sheathing; compression webs require lateral bracing at the spacing assumed for le.
  3. Joint connections are sized from the tabulated member forces using the selected connector system; final metal connector plate sizes must be confirmed against the plate manufacturer’s current ESR.
  4. Bottom chord tension is checked on a net section An based on the selected heel joint connection type; verify An once the joint detail is fixed.
  5. Unbalanced snow (ASCE 7 §7.6), drift, wind uplift, and seismic load cases are not considered in this sheet.
  6. Deflection is computed by virtual work using E for all members; the long-term dead load component is amplified by Kcr = 1.5 per NDS Appendix F.
  7. Permanent lateral restraint and diagonal bracing per BCSI/TPI is required for the installed truss system.