wood beam analysis - university of michigan

WoodColumnAnalysisHomework 03Lab 02

WoodColumnAnalysisHomework 03

WoodColumnAnalysisHomework 03

For the given dimensioned lumber column with 1/3 point weak axis bracing, determine the maximum load capacity of the given load type. Moisture Content = 15%. Ct = Ci = 1.0. Assume pinned end conditions (K=1).

Datasheet Wood SpeciesWood GradeStrong Axis Length, L1Weak Axis Length, L2Narrow Width, d2Wide Width, d1Load Type

HEM-FIRSelect Structural

18FT6FT4IN

10INLive Load

Questions 1. Tabulated Allow. Compressive Stress, Fc2. Tabulated Minimum Modulus of Elasticity, Emin3. Load Duration Factor, CD4. Size Factor, CF5. Factored Allow. Modulus of Elasticity, E’min6. Strong Axis (x-x) Slenderness Ratio, lex/d17. Weak Axis (y-y) Slenderness Ratio, ley/d28. Controlling Slenderness Ratio, le/d9. Critical Buckling Design Value for Compression, FcE10. Reference Compression Design Value, Fc*11. Constant for Sawn Lumber, c12. Column Stability Factor, CP13. Factored Allow. Compressive Stress, F'c14. Column Area, A15. Maximum Allowable Axial Load Capacity, Pmax

Main Steps1. Tabulated Fc, Emin2. Slenderness Ratios3. Adjustment Factors

for Fc and Emin4. Max. Allowable Stress

F’c5. Max. Allowable

Compressive Load, Pmax




18FT6FT4IN

10INLive Load


1. Tabulated Fc, Emin

Related Questions 1. Tabulated Allow. Compressive Stress, Fc2. Tabulated Min. Modulus of Elasticity, Emin



18FT6FT4IN

10INLive Load

1. Tabulated Allow. Compressive Stress, Fc = 1,500 PSI2. Tabulated Min. Modulus of Elasticity, Emin = 580,000 PSI

2. Slenderness Ratios

Related Questions 6. Strong Axis (x-x) Slenderness Ratio, lex/d17. Weak Axis (y-y) Slenderness Ratio, ley/d28. Controlling Slenderness Ratio, le/d

Datasheet Wood SpeciesWood GradeStrong Axis Length, L1Weak Axis Length, L2Narrow Width, d2Wide Width, d1Load TypeTab. Allow. Comp. Stress, FcTab. Min. Mod. Elast., Emin


18FT6FT4IN

10INLive Load1500PSI

580000PSI


Actual size: 3.5” x 9.25”



Datasheet Wood SpeciesWood GradeStrong Axis Length, L1Weak Axis Length, L2Narrow Width, d2Actual Width, d2actualWide Width, d1Actual Width, d1actualLoad TypeTab. Allow. Comp. Stress, FcTab. Min. Mod. Elast., Emin


18FT6FT4IN

3.5IN10IN

9.25INLive Load1500PSI

580000PSI

6. Strong Axis (x-x) Slenderness Ratio, lex/d1= Ke x l1 / d1 = 1.0 x 18 x 12/9.25 = 23.351


Le = Ke x L



Datasheet Wood SpeciesWood GradeStrong Axis Length, L1Weak Axis Length, L2Narrow Width, d2Actual Width, d2actualWide Width, d1Actual Width, d1actualLoad TypeTab. Allow. Comp. Stress, FcTab. Min. Mod. Elast., Emin


18FT6FT4IN

3.5IN10IN

9.25INLive Load1500PSI

580000PSI

7. Weak Axis (y-y) Slenderness Ratio,ley/d2= Ke x l2 / d2 = 1.0 x 6 x 12/3.5 = 20.571

Le = Ke x L



Datasheet Wood SpeciesWood GradeStrong Axis Length, L1Weak Axis Length, L2Narrow Width, d2Wide Width, d1Load TypeTab. Allow. Comp. Stress, FcTab. Min. Mod. Elast., Emin


18FT6FT4IN


580000PSI

8. Controlling Slenderness Ratio, le/d = lex/d1 = 23.351

Le = Ke x L

3. Adjustment Factors for Fc and Emin

Related Questions 3. Load Duration Factor, CD4. Size Factor, CF

Datasheet Wood SpeciesWood GradeStrong Axis Length, L1Weak Axis Length, L2Narrow Width, d2Wide Width, d1Load TypeTab. Allow. Comp. Stress, FcTab. Min. Mod. Elast., EminCt = Ci = 1.0


18FT6FT4IN


580000PSI





18FT6FT4IN


580000PSI

3. Load Duration Factor, CD = 1.0



Datasheet Wood SpeciesWood GradeStrong Axis Length, L1Weak Axis Length, L2Narrow Width, d2Wide Width, d1Moisture ContentLoad TypeTab. Allow. Comp. Stress, FcTab. Min. Mod. Elast., EminCt = Ci = 1.0


18FT6FT4IN

10IN15%

Live Load1500PSI

580000PSI

Wet Service Factor for Fc, CM_c = 1Wet Service Factor for FEmin, CM_Emin = 1





18FT6FT4IN


580000PSI

4. Size Factor, CF= 1





18FT6FT4IN


580000PSI

CT did not applied


Related Questions 5. Factored Allow. Modulus of Elasticity, E’min9. Critical Buckling Design Value for Compression, FcE10. Reference Comression Design Value, Fc*11. Constant for Sawn Lumber, c12. Column Stability Factor, CP

Datasheet Wood SpeciesWood GradeStrong Axis Length, L1Weak Axis Length, L2Narrow Width, d2Wide Width, d1Moisture ContentLoad TypeTab. Allow. Comp. Stress, FcTab. Min. Mod. Elast., EminCD = CM = Ct = CF = Ci = CT = 1.0


18FT6FT4IN

10IN15%

Live Load1500PSI

580000PSI


Related Questions 5. Factored Allow. Modulus of Elasticity, E’min9. Critical Buckling Design Value for Compression, FcE10. Reference Comression Design Value, Fc*11. Constant for Sawn Lumber, c12. Column Stability Factor, CP



18FT6FT4IN

10IN15%

Live Load1500PSI

580000PSI

5. Factored Allow. Modulus of Elasticity, E’min = Emin x CM x Ct x Ci x CT = 580,000PSI


Related Questions 5. Factored Allow. Modulus of Elasticity, E’min9. Critical Buckling Design Value for Compression, FcE10. Reference Compression Design Value, Fc*11. Constant for Sawn Lumber, c12. Column Stability Factor, CP



18FT6FT4IN

10IN15%

Live Load1500PSI

580000PSI

10. Reference Compression Design Value, Fc* = Fc x CD x CM x Ct x CF x Ci = 1500PSI


Related Questions 5. Factored Allow. Modulus of Elasticity, E’min9. Critical Buckling Design Value for Compression, FcE10. Reference Compression Design Value, Fc*11. Constant for Sawn Lumber, c12. Column Stability Factor, CP

Datasheet Wood SpeciesWood GradeStrong Axis Length, L1Weak Axis Length, L2Narrow Width, d2Wide Width, d1Moisture ContentLoad TypeTab. Allow. Comp. Stress, FcTab. Min. Mod. Elast., EminCD = CM = Ct = CF = Ci = CT = 1.0Ref. Comp. Design Value, Fc*Fac. Allow. Modulus E’minCtrl Slenderness Ratio, le/d


18FT6FT4IN

10IN15%

Live Load1500PSI

580000PSI

1500PSI580000PSI

23.351

9. Critical Buckling Design Value for Compression, FcE = 0.822 x 580000 / 23.3512 = 874.357 PSI

11. Constant for Sawn Lumber, c = 0.8

FcE / Fc* = 874.351 / 1500 = 0.58290

12. Column Stability Factor, CP = (1 + 0.58290) / (2 x 0.8)

- √ { [(1+0.58290) / (2 x 0.8)]2 - 0.58290/ 0.8}= 0.489

4. Max. Allowable Stress F’c

Related Questions 13. Factored Allow. Compressive Stress, F'c

Datasheet Wood SpeciesWood GradeStrong Axis Length, L1Weak Axis Length, L2Narrow Width, d2Wide Width, d1Moisture ContentLoad TypeTab. Allow. Comp. Stress, FcTab. Min. Mod. Elast., EminCD = CM = Ct = CF = Ci = CT = 1.0CP = 0.548Ref. Comp. Design Value, Fc*Fac. Allow. Modulus E’minCtrl Slenderness Ratio, le/d


18FT6FT4IN

10IN15%

Live Load1500PSI

580000PSI

1500PSI580000PSI

21.6


13. Factored Allow. Compressive Stress, F’c = Fc* x CP = 1500 x 0.489 = 733.5 PSI

5. Max. Allowable Compressive Load, Pmax

Related Questions 14. Column Area, A15. Maximum Allowable Axial Load Capacity, Pmax

Datasheet Wood SpeciesWood GradeStrong Axis Length, L1Weak Axis Length, L2Narrow Width, d2Wide Width, d1Moisture ContentLoad TypeTab. Allow. Comp. Stress, FcTab. Min. Mod. Elast., EminCD = CM = Ct = CF = Ci = CT = 1.0CP = 0.548Ref. Comp. Design Value, Fc*Fac. Allow. C Stress, F’cFac. Allow. Modulus E’minCtrl Slenderness Ratio, le/d


18FT6FT4IN

10IN15%

Live Load1500PSI

580000PSI

1500PSI822 PSI

580000PSI21.6


14. Column Area, A = 32.38 IN2

5. Max. Allowable Compressive Load, Pmax

Related Questions 14. Column Area, A15. Maximum Allowable Axial Load Capacity, Pmax

Datasheet Wood SpeciesWood GradeStrong Axis Length, L1Weak Axis Length, L2Narrow Width, d2Wide Width, d1Moisture ContentLoad TypeTab. Allow. Comp. Stress, FcTab. Min. Mod. Elast., EminCD = CM = Ct = CF = Ci = CT = 1.0CP = 0.548Ref. Comp. Design Value, Fc*Fac. Allow. C Stress, F’cFac. Allow. Modulus E’minCtrl Slenderness Ratio, le/d


18FT6FT4IN

10IN15%

Live Load1500PSI

580000PSI

1500PSI822 PSI

580000PSI21.6


F’c fc_actual>822 PSI

Allowable Actual

= P/A

F’c = Pmax/A

Pmax = F’c x A

15. Maximum Allowable Axial Load Capacity, Pmax = 733.5 x 32.38 = 23750.73LBS




18FT6FT4IN

10INLive Load


Main Steps1. Tabulated Fc, Emin2. Slenderness Ratios3. Adjustment Factors

for Fc and Emin4. Max. Allowable Stress

F’c5. Max. Allowable

Compressive Load, Pmax

WoodColumnAnalysisLab 02

https://miro.com/app/board/o9J_lUnrvr8=/

Hints 1. Use Weak Axis Data d2 = 0.0625in to calculate r2. Calculate Pcr for three situations3. Calculate L/r for three situations4. Calculate Pmax5. Draw diagram based on (L/r, Pcr), three pairs6. Mark Pmax on the diagram

Keys (Show your steps on your answer sheet)r = 0.018042 in6”: Pcr = 2.298 lbs, L/r = 332.5943”: Pcr = 9.194 lbs, L/r = 166.2971”: Pcr = 82.74 lbs, L/r = 55.432Pmax = 74.141 lbs

Diagram similar to the lab sheet’s diagram, show the points

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wood beam analysis - university of michigan

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