wood beam analysis - university of michigan
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WoodColumnAnalysisHomework 03Lab 02
WoodColumnAnalysisHomework 03
WoodColumnAnalysisHomework 03
WoodColumnAnalysisHomework 03
WoodColumnAnalysisHomework 03
WoodColumnAnalysisHomework 03
WoodColumnAnalysisHomework 03
WoodColumnAnalysisHomework 03
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
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
1. Tabulated Fc, Emin
Related Questions 1. Tabulated Allow. Compressive Stress, Fc2. Tabulated Min. Modulus of Elasticity, Emin
Datasheet Wood SpeciesWood GradeStrong Axis Length, L1Weak Axis Length, L2Narrow Width, d2Wide Width, d1Load Type
HEM-FIRSelect Structural
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
HEM-FIRSelect Structural
18FT6FT4IN
10INLive Load1500PSI
580000PSI
1. Tabulated Fc, Emin
Actual size: 3.5” x 9.25”
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, d2Actual Width, d2actualWide Width, d1Actual Width, d1actualLoad TypeTab. Allow. Comp. Stress, FcTab. Min. Mod. Elast., Emin
HEM-FIRSelect Structural
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
1. Tabulated Fc, Emin
Le = Ke x L
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, d2Actual Width, d2actualWide Width, d1Actual Width, d1actualLoad TypeTab. Allow. Comp. Stress, FcTab. Min. Mod. Elast., Emin
HEM-FIRSelect Structural
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
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
HEM-FIRSelect Structural
18FT6FT4IN
10INLive Load1500PSI
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
HEM-FIRSelect Structural
18FT6FT4IN
10INLive Load1500PSI
580000PSI
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
HEM-FIRSelect Structural
18FT6FT4IN
10INLive Load1500PSI
580000PSI
3. Load Duration Factor, CD = 1.0
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, d1Moisture ContentLoad TypeTab. Allow. Comp. Stress, FcTab. Min. Mod. Elast., EminCt = Ci = 1.0
HEM-FIRSelect Structural
18FT6FT4IN
10IN15%
Live Load1500PSI
580000PSI
Wet Service Factor for Fc, CM_c = 1Wet Service Factor for FEmin, CM_Emin = 1
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
HEM-FIRSelect Structural
18FT6FT4IN
10INLive Load1500PSI
580000PSI
4. Size Factor, CF= 1
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
HEM-FIRSelect Structural
18FT6FT4IN
10INLive Load1500PSI
580000PSI
CT did not applied
3. Adjustment Factors for Fc and Emin
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
HEM-FIRSelect Structural
18FT6FT4IN
10IN15%
Live Load1500PSI
580000PSI
3. Adjustment Factors for Fc and Emin
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
HEM-FIRSelect Structural
18FT6FT4IN
10IN15%
Live Load1500PSI
580000PSI
3. Adjustment Factors for Fc and Emin
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
HEM-FIRSelect Structural
18FT6FT4IN
10IN15%
Live Load1500PSI
580000PSI
5. Factored Allow. Modulus of Elasticity, E’min = Emin x CM x Ct x Ci x CT = 580,000PSI
3. Adjustment Factors for Fc and Emin
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 = 1.0
HEM-FIRSelect Structural
18FT6FT4IN
10IN15%
Live Load1500PSI
580000PSI
10. Reference Compression Design Value, Fc* = Fc x CD x CM x Ct x CF x Ci = 1500PSI
3. Adjustment Factors for Fc and Emin
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
HEM-FIRSelect Structural
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
HEM-FIRSelect Structural
18FT6FT4IN
10IN15%
Live Load1500PSI
580000PSI
1500PSI580000PSI
21.6
3. Adjustment Factors for Fc and Emin
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
HEM-FIRSelect Structural
18FT6FT4IN
10IN15%
Live Load1500PSI
580000PSI
1500PSI822 PSI
580000PSI21.6
4. Max. Allowable Stress F’c
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
HEM-FIRSelect Structural
18FT6FT4IN
10IN15%
Live Load1500PSI
580000PSI
1500PSI822 PSI
580000PSI21.6
4. Max. Allowable Stress F’c
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
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
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
Watch the Video First !