Huntly Christie 1/26/2018 Christie Lites 100 Carson Street Toronto, ON M8W3R9

Size: px

Start display at page:

Download "Huntly Christie 1/26/2018 Christie Lites 100 Carson Street Toronto, ON M8W3R9"

Emil Higgins
5 years ago
Views:

Huntly Christie 1/26/2018 Christie Lites 100 Carson Street Toronto, ON M8W3R9 Structural Analysis for 20.5x20.5 Plated Box Truss Tables CRE Project # 16.614.

.. Section 3 We trust this information is suitable for your needs at this time. If you have any questions, please do not hesitate to contact our office.

1 Huntly Christie 1/26/2018 Christie Lites 100 Carson Street Toronto, ON M8W3R9 Structural Analysis for 20.5x20.5 Plated Box Truss Tables CRE Project # Table of Contents for Analysis Package General Notes... Section 1 Truss Allowable Loading Tables... Section x20.5 Plated Box Truss Calculations... Section 3 We trust this information is suitable for your needs at this time. If you have any questions, please do not hesitate to contact our office. Regards, Clark Reder Engineering Inc. 6/30/ /26/2018 Jeffrey M. Reder, P.E. Eric Kelly Clark Reder Engineering, Inc Mosteller Lane, West Chester, OH Phone (513) Fax (513)

2 SECTION 1 Clark Reder Engineering, Inc Mosteller Lane, West Chester, OH Phone (513) Fax (513)

GENERAL STRUCTURAL NOTES CODES AND REFERENCE 1. 2012 INTERNATIONAL BUILDING CODE 2. ASCE 7-10 MINIMUM DESIGN LOADS FOR BUILDINGS AND OTHER STRUCTURES 3.

3 GENERAL STRUCTURAL NOTES CODES AND REFERENCE INTERNATIONAL BUILDING CODE 2. ASCE 7-10 MINIMUM DESIGN LOADS FOR BUILDINGS AND OTHER STRUCTURES 3. ASCE DESIGN LOADS ON STRUCTURES UNDER CONSTRUCTION 4. ALUMINUM DESIGN MANUAL, 2010 EDITION DESIGN LOADS 1. DEAD LOAD: SELFWEIGHT OF ALUMINUM TRUSS 2. RIGGING LOADS: SEE ATTACHED ALLOWABLE LOADING CONSTRUCTION AND SAFETY 1. ENGINEER SHALL NOT BE RESPONSIBLE FOR MEANS, METHODS, OR SEQUENCE OF CONSTRUCTION UNLESS SPECIFICALLY STATED ON THE DRAWINGS. 2. ENGINEER HAS DESIGNED THE STRUCTURES FOR THEIR FINAL AS-BUILT CONDITION. ENGINEER IS NOT RESPONSIBLE FOR TEMPORARY STABILITY OF STRUCTURES DURING ERECTION UNLESS SPECIFICALLY STATED ON THE DRAWINGS. 3. STRUCTURE HAS BEEN DESIGNED AS A TEMPORARY STRUCTURE THAT SHALL BE IN PLACE FOR LESS THAN 6 WEEKS. ALUMINUM 1. ALUMINUM SHALL CONFORM TO THE FOLLOWING UNLESS NOTED OTHERWISE ON THE DRAWINGS: A. MEMBER ALLOY: 6061-T6 B. CHANNELS, PLATES AND SHEETS: T6 C. WELD FILLER ALLOW: ALL DETAILING, FABRICATION AND ERECTION SHALL CONFORM TO THE ALUMINUM ASSOCIATION ALUMINUM DESIGN MANUAL, CURRENT EDITION. 3. WELDING SHALL BE IN ACCORDANCE WITH THE AMERICAN WELDING SOCIETY LATEST EDITION. 4. FIELD CONNECTIONS SHALL BE BOLTED UNLESS SPECIFIED OTHERWISE ON THE DRAWINGS. 5. ALUMINUM TRUSS TO ALUMINUM TRUSS CONNECTION BOLTS: 5/8 DIAMETER GRADE 8 BOLTS ALLOWABLE LOADING GUIDELINES 1. EACH LOAD INDICATED IN THE TABLE IS INDEPENDENT OF THE OTHER LOADS AND IS NOT ADDITIVE TO ANY OTHER LOAD. 2. CARE SHOULD BE TAKEN WHEN APPLYING LOADS AS LOADING OF ONE TRUSS MAY INDUCE LOAD ON ANOTHER TRUSS RESULTING IN AN OVERLOAD SITUATION. 3. THE UNIFORMLY DISTRIBUTED LOAD IS ONLY APPLICABLE IF THE LOAD IS APPLIED EVENLY OVER THE ENTIRE LENGTH OF THE TRUSS. 4. SELFWEIGHT OF THE TRUSS HAS BEEN INCLUDED IN THE CALCULATION OF THE ALLOWABLE LOADS. 5. ALL LOADS SHALL BE APPLIED AT TRUSS PANEL POINTS ONLY. ON BOX TRUSS, PANEL POINTS ARE LOCATIONS WHERE THE CHORD IS BRACED BOTH VERTICALLY AND HORIZONTALLY. ON LADDER TRUSS, PANEL POINTS ARE LOCATIONS WHERE THE CHORD IS BRACED BY A VERTICAL OR DIAGONAL MEMBER. 6. BRIDLES ARE NOT PERMITTED UNLESS APPROVED IN WRITING BY THE ENGINEER OF RECORD. 7. ALLOWABLE LOADS INDICATED ARE FOR GENERAL GUIDANCE ONLY. ALL RIGGING PLOTS SHOULD BE EVALUATED BY A LICENSED STRUCTURAL ENGINEER PRIOR TO HANGING ANY RIGGING LOADS. 8. NO DYNAMIC OR SHOCK LOADS HAVE BEEN TAKEN INTO ACCOUNT. INSPECTIONS 1. ALL TRUSS UNITS, SCAFFOLD AND/OR OTHER RIGGING EQUIPMENT SHALL BE VISUALLY INSPECTED PRIOR TO ERECTION. DAMAGED OR CORRODED EQUIPMENT SHALL NOT BE USED. FIELD MODIFICATIONS SHALL BE APPROVED BY THE ENGINEER OF RECORD PRIOR TO INSTALLATION. Clark Reder Engineering, Inc Mosteller Ln; West Chester OH Phone (513) Fax (513)

4 SECTION 2 Clark Reder Engineering, Inc Mosteller Lane, West Chester, OH Phone (513) Fax (513)

DIAGONAL 8'-0" CHORD HORIZONTAL TOP VIEW 1'-8 1 2" CHORD DIAGONAL DIAGONAL 1'-8 1 2" 1'-8 1 2" 1'-8 1 2" 3D VIEW END PLATES 8'-0" CHORD VERTICAL END TUBE END VIEW END PLATES SIDE VIEW END TUBE END

5 DIAGONAL 8'-0" CHORD HORIZONTAL TOP VIEW 1'-8 1 2" CHORD DIAGONAL DIAGONAL 1'-8 1 2" 1'-8 1 2" 1'-8 1 2" 3D VIEW END PLATES 8'-0" CHORD VERTICAL END TUBE END VIEW END PLATES SIDE VIEW END TUBE END PLATES 20.5"x20.5" BOLT PLATE TRUSS TABLE UNIFORMLY DISTRIBUTED LOAD CENTER POINT LOAD THIRD POINT LOAD QUARTER POINT LOAD FIFTH POINT LOAD TRUSS SPAN LOAD DEFLECTION LOAD DEFLECTION LOAD DEFLECTION LOAD DEFLECTION LOAD DEFLECTION 8'-0" 840 lb/ft in 3,625 lbs in 2,550 lbs in 1,760 lbs in 1,540 lbs in 16'-0" 210 lb/ft in 1,750 lbs in 1,275 lbs in 850 lbs in 700 lbs in 24'-0" 100 lb/ft in 1,525 lbs in 800 lbs in 675 lbs in 475 lbs in 32'-0" 45 lb/ft in 750 lbs in 550 lbs in 375 lbs in 300 lbs in 40'-0" 25 lb/ft in 625 lbs in 400 lbs in 275 lbs in 200 lbs in 48'-0" 15 lb/ft in 375 lbs in 275 lbs in 185 lbs in 155 lbs in DIAGONALS HORIZONTALS VERTICALS CHORDS END TUBE END PLATES PARTS LIST NOTES: 1. ALL ALUMINUM IS 6061-T6 2. WELD FILLER " x1/8" PIPE 2" x1/8" PIPE 2" x1/8" PIPE 2" x1/8" PIPE 2" x1/8" PIPE PLATE 3/8" TABLE USAGE NOTES: 1. THE TRUSS IS SUPPORTING VERTICAL LOADS ONLY, I.E. THE TRUSS LADDERS ARE ORIENTED VERTICALLY AND NO LATERAL LOADS ARE APPLIED TO THE TRUSS. 2. THE TRUSS WAS ANALYZED AS A SIMPLE SPAN BEAM WITH SUPPORTS AT TRUSS ENDS ONLY. 3. THE TRUSS HAS BEEN ANALYZED FOR STATIC LOADS ONLY. 4. ALL LOADS ARE APPLIED CENTERED BETWEEN THE LADDERS. 5. ALL LOADS AND SUPPORTS ARE TO BE LOCATED AT THE PANEL POINTS OF THE TRUSS ONLY. 6. SELF WEIGHT HAS BEEN CONSIDERED IN THE ANALYSIS OF THE TRUSS. 7. MAXIMUM DEFLECTION LIMITED TO SPAN/ ALLOWABLE LOADS BASED ON 2010 ALUMINUM DESIGN MANUAL. CHRISTIE LITES 20.5"x20.5" BOLT PLATE TRUSS 6/7/2016 SINGLE USE Mosteller Lane West Chester, OH DATE: CRE PROJECT NO: (1) DRAWN BY: 20.5"X20.5" BOLT PLATE TRUSS 8'-0" INCREMENTS EPK/DDL ST1.1

6 DIAGONAL 8'-0" CHORD HORIZONTAL TOP VIEW 1'-8 1 2" CHORD DIAGONAL DIAGONAL 1'-8 1 2" 1'-8 1 2" 1'-8 1 2" 3D VIEW END PLATES 8'-0" CHORD VERTICAL END TUBE END VIEW END PLATES SIDE VIEW END TUBE END PLATES 20.5"x20.5" BOLT PLATE TRUSS TABLE UNIFORMLY DISTRIBUTED LOAD CENTER POINT LOAD THIRD POINT LOAD QUARTER POINT LOAD FIFTH POINT LOAD TRUSS SPAN LOAD DEFLECTION LOAD DEFLECTION LOAD DEFLECTION LOAD DEFLECTION LOAD DEFLECTION 8'-0" 714 lb/ft in 3,081 lbs in 2,168 lbs in 1,496 lbs in 1,309 lbs in 16'-0" 179 lb/ft in 1,488 lbs in 1,084 lbs in 723 lbs in 595 lbs in 24'-0" 85 lb/ft in 1,296 lbs in 680 lbs in 574 lbs in 404 lbs in 32'-0" 38 lb/ft in 638 lbs in 468 lbs in 319 lbs in 255 lbs in 40'-0" 21 lb/ft in 531 lbs in 340 lbs in 234 lbs in 170 lbs in 48'-0" 13 lb/ft in 319 lbs in 234 lbs in 157 lbs in 132 lbs in DIAGONALS HORIZONTALS VERTICALS CHORDS END TUBE END PLATES PARTS LIST NOTES: 1. ALL ALUMINUM IS 6061-T6 2. WELD FILLER " x1/8" PIPE 2" x1/8" PIPE 2" x1/8" PIPE 2" x1/8" PIPE 2" x1/8" PIPE PLATE 3/8" TABLE USAGE NOTES: 1. THE TRUSS IS SUPPORTING VERTICAL LOADS ONLY, I.E. THE TRUSS LADDERS ARE ORIENTED VERTICALLY AND NO LATERAL LOADS ARE APPLIED TO THE TRUSS. 2. THE TRUSS WAS ANALYZED AS A SIMPLE SPAN BEAM WITH SUPPORTS AT TRUSS ENDS ONLY. 3. THE TRUSS HAS BEEN ANALYZED FOR STATIC LOADS ONLY. 4. ALL LOADS ARE APPLIED CENTERED BETWEEN THE LADDERS. 5. ALL LOADS AND SUPPORTS ARE TO BE LOCATED AT THE PANEL POINTS OF THE TRUSS ONLY. 6. SELF WEIGHT HAS BEEN CONSIDERED IN THE ANALYSIS OF THE TRUSS. 7. MAXIMUM DEFLECTION LIMITED TO SPAN/ ALLOWABLE LOADS BASED ON 2010 ALUMINUM DESIGN MANUAL. ALL CAPACITIES ARE REDUCED TO 0.85 PER ANSI E FOR REPETITIVE USE MEMBERS CHRISTIE LITES 20.5"x20.5" BOLT PLATE TRUSS 6/7/2016 REPETITIVE USE Mosteller Lane West Chester, OH DATE: CRE PROJECT NO: (1) DRAWN BY: 20.5"X20.5" BOLT PLATE TRUSS 8'-0" INCREMENTS EPK/DDL ST1.2

7 SECTION 3 Clark Reder Engineering, Inc Mosteller Lane, West Chester, OH Phone (513) Fax (513)

8 Clark-Reder Engineering, Inc Mosteller Lane Cincinnati, OH Phone (513) Fax (513) End Plated 2 x 125 wall - Round Pipe (Chords) Location: Anywhere, USA Codes and Referenced Standards 2012 International Building Code and 2013 California Building Code Aluminum Design Manual, 2010 ed. American Society of Civil Engineers 7-10 (ASCE 7-10) "Minimum Design Loads for Buildings and Other Structures" ANSI E "Manufacture and Use of Aluminum Trusses and Towers" Project Description Provide allowable loading tables for 20.5 x 20.5 truss. Pipe Properties Pipe diameter: D := 2.0in Pipe thickness: t := 0.125in Aluminum alloy: Alloy := Unbraced length (includes K-factor): L b := 14.55in Pipe Cross Section Properties D Inner diameter: D 1 := D 2 t = 1.75 in Radius: R := = 2 π D 4 4 D 1 Moment of inertia: I x := = in 4 Area: 1.00 in π D 2 2 D 1 Area := = 4 I x r y := = in Area Elastic section π D 4 4 D 1 Radius of gyration: modulus: S x := = 32 D Alloy Properties in in 3 Safety Factors Buckling Constants Project:20.5x " Equilateral Triangle CRE Project #: #: of 8 Engineer: TMK 6/7/2016

9 Clark-Reder Engineering, Inc Mosteller Lane Cincinnati, OH Phone (513) Fax (513) Unwelded Welded Ultimate tensile strength: F tu = ksi F tuw = ksi Tensile yield strength: F ty = ksi F tyw = ksi Compressive yield strength: F cy = ksi F cyw = ksi Shear yield strength: F sy = ksi F syw = 9.00 ksi Modulus of elasticity: E a = ksi E a = ksi End Weld Tension Capacity Section D.2a: Welded or unwelded: Weld D2a := 1 Allowable yield stress: F y_d2a := F Ω ty if Weld D2a = 1 F y_d2a = 9.09 ksi ty F tyw otherwise Allowable tension force: T n_d2a := F y_d2a Area T n_d2a = 6.69 kip Section D.2b: Welded or unwelded: Weld D2b := 1 Allowable yield stress: F y_d2b := F Ω tu if Weld D2b = 1 tu F tuw otherwise F y_d2b = ksi Allowable tension force: T n_d2b := F y_d2b Area T n_d2b = 9.06 kip Project:20.5x " Equilateral Triangle CRE Project #: of 8 Engineer: TMK 6/7/2016

10 Clark-Reder Engineering, Inc Mosteller Lane Cincinnati, OH Phone (513) Fax (513) Tension Summary: Controlling tension capacity: ( ) T n_pipe := min T n_d2a, T n_d2b, T n_weld T n_pipe = 6.69 kip T n_pipe Controlling tension stress: F t_pipe := F Area t_pipe = 9.09 ksi Compression Capacity Section E.3: Welded or unwelded: Weld E3 := Slenderness limit: S 2_E3 := C c if Weld E3 = 1 = 66 C cw otherwise KL/r: KLr := L b = r y Allowable compressive stress: 1 F c_e3 := if KLr < S Ω 2_E3 F c_e3 = ksi c min 0.85 B c D c KLr, F cy if Weld E3 = 1 ( ) ( ) min 0.85 B cw D cw KLr 0.85π 2 E a KLr 2 otherwise, F cy otherwise Allowable axial load: P n_e3 := F c_e3 Area P n_e3 = kip Project:20.5x " Equilateral Triangle CRE Project #: of 8 Engineer: TMK 6/7/2016

11 Clark-Reder Engineering, Inc Mosteller Lane Cincinnati, OH Phone (513) Fax (513) Section B.5.4.5: Welded or unwelded: Weld B545 := 2 B t F cy Slenderness limits: S 1_B545 := D t if 2 B tw F cyw D tw Weld B545 = 1 otherwise = 46 S 2_B545 := C t if Weld B545 = 1 = 390 C tw otherwise Rb/t: Rbt := R t = 8.00 Allowable compressive stress: 1 F c_b545 := if Weld Ω B545 = 1 F c_b545 = 9.09 ksi c F cy if Rbt < S 1_B545 π 2 E a 16 Rbt 1 + B t D t Rbt 2 Rbt 35 if otherwise Rbt > S 2_B545 otherwise F cyw if Rbt < S 1_B545 π 2 E a 16 Rbt Rbt 35 B tw D tw Rbt if otherwise Rbt > S 2_B545 Allowable compressive force: P n_b545 := F c_b545 Area P n_b545 = 6.69 kip Project:20.5x " Equilateral Triangle CRE Project #: #: of 8 Engineer: TMK 6/7/2016

12 Clark-Reder Engineering, Inc Mosteller Lane Cincinnati, OH Phone (513) Fax (513) Compression Summary: ( ) Controlling compression capacity: P n_pipe := min P n_e3, P n_b545, T n_weld P n_pipe = 6.69 kip P n_pipe Controlling compressive stress: F c_pipe := F Area c_pipe = 9.09 ksi Flexure Capacity Section F.8.1.2: Welded or unwelded: Weld F812 := Moment capacity: 1 F b_f8121 := 1.3 F Ω ty if Weld F812 = 1 Tensile yielding: F by b_f8121 = ksi 1.3 F tyw otherwise 1 F tu Tensile rupture: F b_f8122 := 1.42 if Weld Ω bu k F812 = 1 t F b_f8122 = ksi F tuw 1.42 k t otherwise Allowable flexural capacity: ( ) S x M n_f812 := min F b_f812 M n_f812 = 3.84 kip in Section F.6.1: Welded or unwelded: Weld F61 := Compressive yielding: M n_f611 := 1.17 F cy S x Ω by = 8.07 kip in 1.17 F ty S x Tensile yielding: M n_f612 := Ω by = 8.07 kip in 1.24 F tu S x Tensile rupture: M n_f613 := k t Ω bu = 8.68 kip in Flexural capacity: M n_f61 min( M n_f61 ) := M n_f61 = 8.07 kip in Project:20.5x " Equilateral Triangle CRE Project #: #: of 8 Engineer: TMK 6/7/2016

13 Clark-Reder Engineering, Inc Mosteller Lane Cincinnati, OH Phone (513) Fax (513) Section F.6.2: Welded or unwelded: Weld F62 := 2 B tb B t Slenderness limits: S 1_F62 := D tb D t B tbw B tw D tbw D tw if 2 Weld F62 = 1 otherwise = 121 S 2_F62 := C t if Weld F62 = 1 = 390 C tw otherwise Rb/t: Rbt = 8.00 Allowable flexural stress: 1 F b_f62 := if Weld Ω F62 = 1 F b_f62 = ksi by B tb D tb Rbt if Rbt < S 1_F62 π 2 E a 16 Rbt 1 + B t D t Rbt 2 Rbt 35 if otherwise Rbt > S 2_F62 otherwise B tbw D tbw Rbt if Rbt < S 1_F62 π 2 E a 16 Rbt Rbt 35 B tw D tw Rbt if otherwise Rbt > S 2_F62 Allowable flexural capacity: M n_f62 := F b_f62 S x M n_f62 = 4.89 kip in Project:20.5x " Equilateral Triangle CRE Project #: of 8 Engineer: TMK 6/7/2016

14 Clark-Reder Engineering, Inc Mosteller Lane Cincinnati, OH Phone (513) Fax (513) Flexural Summary: ( ) Controlling flexural capacity: M n_pipe := min M n_f812, M n_f61, M n_f62 M n_pipe = 3.84 kip in M n_pipe Controlling flexural stress: F b_pipe := F S b_pipe = ksi x Shear capacity Section G.3: Welded or unwelded: Weld G3 := 1.3 B s F sy Slenderness limits: S 1_G3 := 1.63 D s if Weld G3 = 1 = B sw F syw 1.63 D sw otherwise S 2_G3 := C s 1.25 if Weld G3 = 1 = 126 C sw 1.25 otherwise Length of tube from maximum to zero force: L v := 12in Lv λt: λ t := 2.9 ( Rbt) = R Project:20.5x " Equilateral Triangle CRE Project #: #: of 8 Engineer: TMK 6/7/2016

15 Clark-Reder Engineering, Inc Mosteller Lane Cincinnati, OH Phone (513) Fax (513) Allowable shear stress: 1 F v_g3 := if Weld Ω G3 = 1 F v_g3 = 5.45 ksi v F sy if λ t < S 1_G3 1.3π 2 E a ( 1.25λ t ) 2 if λ t > S 2_G3 1.3 B s 1.63 D s λ t otherwise otherwise F syw if λ t < S 1_G3 1.3π 2 E a ( 1.25λ t ) 2 if λ t > S 2_G3 1.3 B sw 1.63 D sw λ t otherwise Allowable shear capacity: Area V n_g3 := F v_g3 V 2 n_g3 = 2.01 kip Shear Summary: ( ) Controlling shear capacity: V n_pipe := min V n_g3, V n_weld V n_pipe = 2.01 kip V n_pipe Controlling shear stress: F v_pipe := 2 F Area v_pipe = 5.45 ksi Component summary: Allowable Force Allowable Stress Tension capacity: T n_pipe = 6.69 kip F t_pipe = 9.09 ksi Compressive capacity: P n_pipe = 6.69 kip F c_pipe = 9.09 ksi Moment capacity: M n_pipe = 3.84 kip in F b_pipe = ksi Shear capacity: V n_pipe = 2.01 kip F v_pipe = 5.45 ksi Project: Project:20.5x " Equilateral Triangle CRE CRE Project Project #: #: of 8 Engineer: TMK 6/7/2016

16 Clark-Reder Engineering, Inc Mosteller Lane Cincinnati, OH Phone (513) Fax (513) End Plated 2 x 125 wall - Round Pipe (Horizontals) Location: Anywhere, USA Codes and Referenced Standards 2012 International Building Code and 2013 California Building Code Aluminum Design Manual, 2010 ed. American Society of Civil Engineers 7-10 (ASCE 7-10) "Minimum Design Loads for Buildings and Other Structures" ANSI E "Manufacture and Use of Aluminum Trusses and Towers" Project Description Provide allowable loading tables for 12x18 box truss. Pipe Properties Pipe diameter: D := 2.0in Pipe thickness: t := 0.125in Aluminum alloy: Alloy := Unbraced length (includes K-factor): L b := 14.75in Pipe Cross Section Properties D Inner diameter: D 1 := D 2 t = 1.75 in Radius: R := = 2 π D 4 4 D 1 Moment of inertia: I x := = in 4 Area: 1.00 in π D 2 2 D 1 Area := = 4 I x r y := = in Area Elastic section π D 4 4 D 1 Radius of gyration: modulus: S x := = 32 D Alloy Properties in in 3 Safety Factors Buckling Constants Project:20.5x " Equilateral Triangle CRE Project #: of 8 Engineer: TMK 6/7/2016

17 Clark-Reder Engineering, Inc Mosteller Lane Cincinnati, OH Phone (513) Fax (513) Unwelded Welded Ultimate tensile strength: F tu = ksi F tuw = ksi Tensile yield strength: F ty = ksi F tyw = ksi Compressive yield strength: F cy = ksi F cyw = ksi Shear yield strength: F sy = ksi F syw = 9.00 ksi Modulus of elasticity: E a = ksi E a = ksi End Weld Tension Capacity Section D.2a: Welded or unwelded: Weld D2a := 1 Allowable yield stress: F y_d2a := F Ω ty if Weld D2a = 1 F y_d2a = 9.09 ksi ty F tyw otherwise Allowable tension force: T n_d2a := F y_d2a Area T n_d2a = 6.69 kip Section D.2b: Welded or unwelded: Weld D2b := 1 Allowable yield stress: F y_d2b := F Ω tu if Weld D2b = 1 tu F tuw otherwise F y_d2b = ksi Allowable tension force: T n_d2b := F y_d2b Area T n_d2b = 9.06 kip Project:20.5x " Equilateral Triangle CRE Project #: of 8 Engineer: TMK 6/7/2016

18 Clark-Reder Engineering, Inc Mosteller Lane Cincinnati, OH Phone (513) Fax (513) Tension Summary: Controlling tension capacity: ( ) T n_pipe := min T n_d2a, T n_d2b, T n_weld T n_pipe = 6.69 kip T n_pipe Controlling tension stress: F t_pipe := F Area t_pipe = 9.09 ksi Compression Capacity Section E.3: Welded or unwelded: Weld E3 := Slenderness limit: S 2_E3 := C c if Weld E3 = 1 = 66 C cw otherwise KL/r: KLr := L b = r y Allowable compressive stress: 1 F c_e3 := if KLr < S Ω 2_E3 F c_e3 = ksi c min 0.85 B c D c KLr, F cy if Weld E3 = 1 ( ) ( ) min 0.85 B cw D cw KLr 0.85π 2 E a KLr 2 otherwise, F cy otherwise Allowable axial load: P n_e3 := F c_e3 Area P n_e3 = kip Project:20.5x " Equilateral Triangle CRE Project #: of 8 Engineer: TMK 6/7/2016

19 Clark-Reder Engineering, Inc Mosteller Lane Cincinnati, OH Phone (513) Fax (513) Section B.5.4.5: Welded or unwelded: Weld B545 := 2 B t F cy Slenderness limits: S 1_B545 := D t if 2 B tw F cyw D tw Weld B545 = 1 otherwise = 46 S 2_B545 := C t if Weld B545 = 1 = 390 C tw otherwise Rb/t: Rbt := R t = 8.00 Allowable compressive stress: 1 F c_b545 := if Weld Ω B545 = 1 F c_b545 = 9.09 ksi c F cy if Rbt < S 1_B545 π 2 E a 16 Rbt 1 + B t D t Rbt 2 Rbt 35 if otherwise Rbt > S 2_B545 otherwise F cyw if Rbt < S 1_B545 π 2 E a 16 Rbt Rbt 35 B tw D tw Rbt if otherwise Rbt > S 2_B545 Allowable compressive force: P n_b545 := F c_b545 Area P n_b545 = 6.69 kip Project:20.5x " Equilateral Triangle CRE Project #: of 8 Engineer: TMK 6/7/2016

20 Clark-Reder Engineering, Inc Mosteller Lane Cincinnati, OH Phone (513) Fax (513) Compression Summary: ( ) Controlling compression capacity: P n_pipe := min P n_e3, P n_b545, T n_weld P n_pipe = 6.69 kip P n_pipe Controlling compressive stress: F c_pipe := F Area c_pipe = 9.09 ksi Flexure Capacity Section F.8.1.2: Welded or unwelded: Weld F812 := Moment capacity: 1 F b_f8121 := 1.3 F Ω ty if Weld F812 = 1 Tensile yielding: F by b_f8121 = ksi 1.3 F tyw otherwise 1 F tu Tensile rupture: F b_f8122 := 1.42 if Weld Ω bu k F812 = 1 t F b_f8122 = ksi F tuw 1.42 k t otherwise Allowable flexural capacity: ( ) S x M n_f812 := min F b_f812 M n_f812 = 3.84 kip in Section F.6.1: Welded or unwelded: Weld F61 := Compressive yielding: M n_f611 := 1.17 F cy S x Ω by = 8.07 kip in 1.17 F ty S x Tensile yielding: M n_f612 := Ω by = 8.07 kip in 1.24 F tu S x Tensile rupture: M n_f613 := k t Ω bu = 8.68 kip in Flexural capacity: M n_f61 min( M n_f61 ) := M n_f61 = 8.07 kip in Project:20.5x " Equilateral Triangle CRE Project #: of 8 Engineer: TMK 6/7/2016

21 Clark-Reder Engineering, Inc Mosteller Lane Cincinnati, OH Phone (513) Fax (513) Section F.6.2: Welded or unwelded: Weld F62 := 2 B tb B t Slenderness limits: S 1_F62 := D tb D t B tbw B tw D tbw D tw if 2 Weld F62 = 1 otherwise = 121 S 2_F62 := C t if Weld F62 = 1 = 390 C tw otherwise Rb/t: Rbt = 8.00 Allowable flexural stress: 1 F b_f62 := if Weld Ω F62 = 1 F b_f62 = ksi by B tb D tb Rbt if Rbt < S 1_F62 π 2 E a 16 Rbt 1 + B t D t Rbt 2 Rbt 35 if otherwise Rbt > S 2_F62 otherwise B tbw D tbw Rbt if Rbt < S 1_F62 π 2 E a 16 Rbt Rbt 35 B tw D tw Rbt if otherwise Rbt > S 2_F62 Allowable flexural capacity: M n_f62 := F b_f62 S x M n_f62 = 4.89 kip in Project:20.5x " Equilateral Triangle CRE Project #: #: of 8 Engineer: TMK 6/7/2016

22 Clark-Reder Engineering, Inc Mosteller Lane Cincinnati, OH Phone (513) Fax (513) Flexural Summary: ( ) Controlling flexural capacity: M n_pipe := min M n_f812, M n_f61, M n_f62 M n_pipe = 3.84 kip in M n_pipe Controlling flexural stress: F b_pipe := F S b_pipe = ksi x Shear capacity Section G.3: Welded or unwelded: Weld G3 := 1.3 B s F sy Slenderness limits: S 1_G3 := 1.63 D s if Weld G3 = 1 = B sw F syw 1.63 D sw otherwise S 2_G3 := C s 1.25 if Weld G3 = 1 = 126 C sw 1.25 otherwise Length of tube from maximum to zero force: L v := 12in Lv λt: λ t := 2.9 ( Rbt) = R Project:20.5x " Equilateral Triangle CRE Project #: of 8 Engineer: TMK 6/7/2016

23 Clark-Reder Engineering, Inc Mosteller Lane Cincinnati, OH Phone (513) Fax (513) Allowable shear stress: 1 F v_g3 := if Weld Ω G3 = 1 F v_g3 = 5.45 ksi v F sy if λ t < S 1_G3 1.3π 2 E a ( 1.25λ t ) 2 if λ t > S 2_G3 1.3 B s 1.63 D s λ t otherwise otherwise F syw if λ t < S 1_G3 1.3π 2 E a ( 1.25λ t ) 2 if λ t > S 2_G3 1.3 B sw 1.63 D sw λ t otherwise Allowable shear capacity: Area V n_g3 := F v_g3 V 2 n_g3 = 2.01 kip Shear Summary: ( ) Controlling shear capacity: V n_pipe := min V n_g3, V n_weld V n_pipe = 2.01 kip V n_pipe Controlling shear stress: F v_pipe := 2 F Area v_pipe = 5.45 ksi Component summary: Allowable Force Allowable Stress Tension capacity: T n_pipe = 6.69 kip F t_pipe = 9.09 ksi Compressive capacity: P n_pipe = 6.69 kip F c_pipe = 9.09 ksi Moment capacity: M n_pipe = 3.84 kip in F b_pipe = ksi Shear capacity: V n_pipe = 2.01 kip F v_pipe = 5.45 ksi Project:20.5x " Equilateral Triangle CRE Project #: #: of 8 Engineer: TMK 6/7/2016

24 Clark-Reder Engineering, Inc Mosteller Lane Cincinnati, OH Phone (513) Fax (513) End Plated 20.5 x 20.5 Box Truss- Round Pipe (Diags) Location: Anywhere, USA Codes and Referenced Standards 2012 International Building Code and 2013 California Building Code Aluminum Design Manual, 2010 ed. American Society of Civil Engineers 7-10 (ASCE 7-10) "Minimum Design Loads for Buildings and Other Structures" ANSI E "Manufacture and Use of Aluminum Trusses and Towers" Project Description Provide allowable loading tables for 20.5 x 20.5 box truss. Pipe Properties Pipe diameter: D := 1.0in Pipe thickness: t := 0.125in Aluminum alloy: Alloy := Unbraced length (includes K-factor): L b := in Pipe Cross Section Properties Inner diameter: D D 1 := D 2t = 0.75 in Radius: R := = 2 π D 4 4 D 1 Moment of inertia: I x := = in 4 Area: 0.50 in π D 2 2 D 1 Area := = 4 I x r y := = in Area Elastic section π D 4 4 D 1 Radius of gyration: modulus: S x := = 32D Alloy Properties 0.344in in 3 Safety Factors Buckling Constants Project:12" Project:20.5x20.5 Equilateral Triangle CRE Project #: of 9 Engineer: TMK 6/7/2016

25 Clark-Reder Engineering, Inc Mosteller Lane Cincinnati, OH Phone (513) Fax (513) Unwelded Welded Ultimate tensile strength: F tu = 42.00ksi F tuw = 24.00ksi Tensile yield strength: F ty = 35.00ksi F tyw = 15.00ksi Compressive yield strength: F cy = 35.00ksi F cyw = 15.00ksi Shear yield strength: F sy = 21.00ksi F syw = 9.00ksi Modulus of elasticity: E a = 10100ksi E a = 10100ksi End Weld Tension Capacity Section D.2a: Welded or unwelded: Weld D2a := 1 Allowable yield stress: F y_d2a := F Ω ty if Weld D2a = 1 F y_d2a = 9.09ksi ty F tyw otherwise Allowable tension force: T n_d2a := F y_d2a Area T n_d2a = 3.12kip Section D.2b: Welded or unwelded: Weld D2b := 1 Allowable yield stress: F y_d2b := F Ω tu if Weld D2b = 1 tu F tuw otherwise F y_d2b = 12.31ksi Allowable tension force: T n_d2b := F y_d2b Area T n_d2b = 4.23kip Project:12" Project:20.5x20.5 Equilateral Triangle CRE Project #: of 9 Engineer: TMK 6/7/2016

26 Clark-Reder Engineering, Inc Mosteller Lane Cincinnati, OH Phone (513) Fax (513) Tension Summary: Controlling tension capacity: ( ) T n_pipe := min T n_d2a, T n_d2b, T n_weld T n_pipe = 3.12kip Controlling tension stress: T n_pipe F t_pipe := F Area t_pipe = 9.09ksi Compression Capacity Section E.3: Welded or unwelded: Weld E3 := Slenderness limit: S 2_E3 := C c if Weld E3 = 1 = 66 C cw otherwise KL/r: KLr := L b = r y Allowable compressive stress: 1 F c_e3 := if KLr < S Ω 2_E3 F c_e3 = 8.82ksi c min 0.85 B c D c KLr, F cy if Weld E3 = 1 ( ) ( ) min 0.85 B cw D cw KLr 0.85π 2 E a KLr 2 otherwise, F cy otherwise Allowable axial load: P n_e3 := F c_e3 Area P n_e3 = 3.03kip Project:12" Project:20.5x20.5 Equilateral Triangle CRE Project #: #: of 9 Engineer: TMK 6/7/2016

27 Clark-Reder Engineering, Inc Mosteller Lane Cincinnati, OH Phone (513) Fax (513) Section B.5.4.5: Welded or unwelded: Weld B545 := 2 B t F cy Slenderness limits: S 1_B545 := D t if 2 B tw F cyw D tw Weld B545 = 1 otherwise = 46 S 2_B545 := C t if Weld B545 = 1 = 390 C tw otherwise Rb/t: Rbt := R t = 4.00 Allowable compressive stress: 1 F c_b545 := if Weld Ω B545 = 1 F c_b545 = 9.09ksi c F cy if Rbt < S 1_B545 π 2 E a 16Rbt 1 + B t D t Rbt 2 Rbt 35 if otherwise Rbt > S 2_B545 otherwise F cyw if Rbt < S 1_B545 π 2 E a 16Rbt Rbt 35 B tw D tw Rbt if otherwise Rbt > S 2_B545 Allowable compressive force: P n_b545 := F c_b545 Area P n_b545 = 3.12kip Project:12" Project:20.5x20.5 Equilateral Triangle CRE Project #: of 9 Engineer: TMK 6/7/2016

28 Clark-Reder Engineering, Inc Mosteller Lane Cincinnati, OH Phone (513) Fax (513) Compression Summary: Controlling compression capacity: Controlling compressive stress: ( ) P n_pipe := min P n_e3, P n_b545, T n_weld P n_pipe = 3.03kip P n_pipe F c_pipe := F Area c_pipe = 8.82ksi Flexure Capacity Section F.8.1.2: Welded or unwelded: Weld F812 := Moment capacity: Tensile yielding: 1 F b_f8121 := 1.3F Ω ty if Weld F812 = 1 by 1.3F tyw otherwise F b_f8121 = 11.82ksi 1 F tu Tensile rupture: F b_f8122 := 1.42 if Weld Ω bu k F812 = 1 t F b_f8122 = 17.48ksi F tuw 1.42 k t otherwise Allowable flexural capacity: ( ) S x M n_f812 := min F b_f812 M n_f812 = 0.79kipin Section F.6.1: Welded or unwelded: Weld F61 := 1.17F cy S x Compressive yielding: M n_f611 := Ω by = 1.67kipin Tensile yielding: 1.17F ty S x M n_f612 := Ω by = 1.67kipin Tensile rupture: 1.24F tu S x M n_f613 := k t Ω bu = 1.79kipin Flexural capacity: M n_f61 min( M n_f61 ) := M n_f61 = 1.67kipin Project:12" Project:20.5x20.5 Equilateral Triangle CRE Project #: of 9 Engineer: TMK 6/7/2016

29 Clark-Reder Engineering, Inc Mosteller Lane Cincinnati, OH Phone (513) Fax (513) Section F.6.2: Welded or unwelded: Weld F62 := 2 B tb B t Slenderness limits: S 1_F62 := D tb D t B tbw B tw D tbw D tw if 2 Weld F62 = 1 otherwise = 121 S 2_F62 := C t if Weld F62 = 1 = 390 C tw otherwise Rb/t: Rbt = 4.00 Allowable flexural stress: 1 F b_f62 := if Weld Ω F62 = 1 F b_f62 = 15.82ksi by B tb D tb Rbt if Rbt < S 1_F62 π 2 E a 16Rbt 1 + B t D t Rbt 2 Rbt 35 if otherwise Rbt > S 2_F62 otherwise B tbw D tbw Rbt if Rbt < S 1_F62 π 2 E a 16Rbt Rbt 35 B tw D tw Rbt if otherwise Rbt > S 2_F62 Allowable flexural capacity: M n_f62 := F b_f62 S x M n_f62 = 1.06kipin Project:12" Project:20.5x20.5 Equilateral Triangle CRE Project #: #: of 9 Engineer: TMK 6/7/2016

30 Clark-Reder Engineering, Inc Mosteller Lane Cincinnati, OH Phone (513) Fax (513) Flexural Summary: Controlling flexural capacity: Controlling flexural stress: ( ) M n_pipe := min M n_f812, M n_f61, M n_f62 M n_pipe = 0.79kipin M n_pipe F b_pipe := F S b_pipe = 11.82ksi x Shear capacity Section G.3: Welded or unwelded: Weld G3 := 1.3B s F sy Slenderness limits: S 1_G3 := 1.63D s if Weld G3 = 1 = B sw F syw 1.63D sw otherwise S 2_G3 := C s 1.25 if Weld G3 = 1 = 126 C sw 1.25 otherwise Length of tube from maximum to zero force: λt: L v := 12in Lv λ t := 2.9 ( Rbt) = R Project:12" Project:20.5x20.5 Equilateral Triangle CRE Project #: of 9 Engineer: TMK 6/7/2016

31 Clark-Reder Engineering, Inc Mosteller Lane Cincinnati, OH Phone (513) Fax (513) Allowable shear stress: 1 F v_g3 := if Weld Ω G3 = 1 F v_g3 = 5.45ksi v F sy if λ t < S 1_G3 1.3π 2 E a ( 1.25λ t ) 2 if λ t > S 2_G3 1.3B s otherwise 1.63D s λ t otherwise F syw if λ t < S 1_G3 1.3π 2 E a ( 1.25λ t ) 2 if λ t > S 2_G3 1.3B sw 1.63D sw λ t otherwise Allowable shear capacity: Area V n_g3 := F v_g3 V 2 n_g3 = 0.94kip Shear Summary: Controlling shear capacity: Controlling shear stress: ( ) V n_pipe := min V n_g3, V n_weld V n_pipe = 0.94kip V n_pipe F v_pipe := 2 F Area v_pipe = 5.45ksi Component summary: Allowable Force Allowable Stress Tension capacity: T n_pipe = 3.12kip F t_pipe = 9.09ksi Compressive capacity: P n_pipe = 3.03kip F c_pipe = 8.82ksi Moment capacity: M n_pipe = 0.79kipin F b_pipe = 11.82ksi Shear capacity: V n_pipe = 0.94kip F v_pipe = 5.45ksi Project:12" Project:20.5x20.5 Equilateral Triangle CRE Project #: of 9 Engineer: TMK 6/7/2016

32 Clark-Reder Engineering, Inc Mosteller Lane Cincinnati, OH Phone (513) Fax (513) Weld of Diagonal to Chord Per J stress on a fillet weld shall be considered to be shear for any direction of applied load. Filler shear ultimate (4043): Base metal shear ultimate welded (6005A-T61): F sufiller := 11.5ksi F suw = 15.00ksi Base metal tensile ultimate welded F tuw = 24.00ksi (6005A-T61): Safety factor n u := 1.95 Angle of diagonal to horizontal: θ d := 45deg 2 D Length of weld L weld π 2 sin( θ d ) 0.5 +( D0.5 ) 2 := ellipse L weld = 3.85in 1 Size of weld S weld := 4 in Weld section modulus: S w := ( 0.5D ) 2 π S w = 0.79 in3 assuming weld is round in 2 Effective throat of fillet weld E weld := S weld E 2 weld = in Nominal weld stress: ( ) F sw := min F sufiller E weld, F suw S weld, F tuw S weld Allowable weld stress: Allowable weld axial & shear capacity: F sw F asw := F n asw = 1.04 kip u in V w := F asw L weld V w = 4.01kip Allowable weld moment capacity: M w := F asw S w M w = 0.82kipin Allowable weld torsional capacity: Tor w := F asw π D ( 0.5D ) Tor w = 1.64kipin Diag axial capacity: Diag moment capacity: controlled by diag compression P d := min T n_pipe, P n_pipe, V w P d = 3.03kip ( ) controlled by diag moment M diag := min M n_pipe, M w M diag = 0.79kipin ( ) Project:20.5x20.5 CRE Project #: of 9 Engineer: TMK 6/7/2016

33 Z Y X Section Sets Bolts Chords Diagonals Horizontals Verticals -.068k -.034k -.068k -.068k -.034k -.068k -.068k -.068k -.068k -.068k -.068k -.068k -.068k -.034k -.034k -.068k -.068k -.034k -.034k -.068k -.068k -.068k -.068k -.068k -.068k -.068k -.068k -.034k -.034k -.068k -.068k -.034k -.034k -.068k -.068k -.068k -.068k -.068k -.068k -.068k -.034k -.034k Loads: LC 2, Selfweight + UDL Clark Reder EPK x20.5 Christie Lite Truss SK - 1 June 7, 2016 at 4:21 PM '-20.5x20.5 Christie Li...

34 Z Y X Section Sets Bolts Chords Diagonals Horizontals Verticals -.763k -.763k Loads: LC 3, Selfweight + CPL Clark Reder EPK x20.5 Christie Lite Truss SK - 2 June 7, 2016 at 4:21 PM '-20.5x20.5 Christie Li...

35 Z Y X Section Sets Bolts Chords Diagonals Horizontals Verticals -.2k -.2k -.2k -.2k -.2k -.2k -.2k -.2k Loads: LC 4, Selfweight + TPL Clark Reder EPK x20.5 Christie Lite Truss SK - 3 June 7, 2016 at 4:22 PM '-20.5x20.5 Christie Li...

36 Z Y X Section Sets Bolts Chords Diagonals Horizontals Verticals -.338k -.338k -.338k -.338k -.338k -.338k Loads: LC 5, Selfweight + QPL Clark Reder EPK x20.5 Christie Lite Truss SK - 4 June 7, 2016 at 4:22 PM '-20.5x20.5 Christie Li...

37 Z Y X Section Sets Bolts Chords Diagonals Horizontals Verticals -.238k -.238k -.238k -.238k -.238k -.238k -.238k -.238k Loads: LC 6, Selfweight + FPL Clark Reder EPK x20.5 Christie Lite Truss SK - 6 June 7, 2016 at 4:23 PM '-20.5x20.5 Christie Li...

38 Basic Load Cases BLC Description Category X Gravity Y Gravity Z Gravity Joint Point Distribut...Area(Me...Surface(... 1 Selfweight None -1 2 Selfweight + UDL None 42 3 Selfweight + CPL None 2 4 Selfweight + TPL None 8 5 Selfweight + QPL None 6 6 Selfweight + FPL None 8 Load Combinations Description Solve PDe...SRSSB...Fa...B...Fa...B...F... B...F...B...F...B...Fa...B...Fa...B...Fa...B...Fa...B...Fa... 1 Selfweight Selfweight + UDL Yes Selfweight + CPL Yes Selfweight + TPL Yes Selfweight + QPL Yes Selfweight + FPL Yes Envelope Joint Displacements 1 N1 max e e e min e e e N2 max e e e min e e e N3 max e e e min e e e N4 max e e e min e e e N5 max e e e min e e e N6 max e e e min e e e N7 max e e e min e e e N8 max e e e min e e e N9 max e e e min e e e N10 max e e e min e e e N11 max e e e min e e e N12 max e e e min e e e N13 max e e e min e e e N14 max e e e min e e e N15 max e e e min e e e N17 max e e e min e e e N18 max e e e min e e e N19 max e e e-3 4 RISA-3D Version [P:\...\...\...\...\...\RISA\ '-20.5x20.5 Christie Lite Truss test.r3d] Page 1

39 36 min e e e N21 max e e e min e e e N22 max e e e min e e e N24 max e e e min e e e N25 max e e e min e e e N27 max e e e min e e e N28 max e e e min e e e N29 max e e e min e e e N30 max e e e min e e e N31 max e e e min e e e N32 max e e e min e e e N33 max e e e min e e e N34 max e e e min e e e N35 max e e e min e e e N36 max e e e min e e e N37 max e e e min e e e N38 max e e e min e e e N39 max e e e min e e e N41 max e e e min e e e N42 max e e e min e e e N43 max e e e min e e e N45 max e e e min e e e N46 max e e e min e e e N48 max e e e min e e e N49 max e e e min e e e N51 max e e e min e e e N52 max e e e min e e e N53 max e e e min e e e N54 max e e e min e e e-3 2 RISA-3D Version [P:\...\...\...\...\...\RISA\ '-20.5x20.5 Christie Lite Truss test.r3d] Page 2

40 93 N57 max e e e min e e e N58 max e e e min e e e N61 max e e e min e e e N62 max e e e min e e e N65 max e e e min e e e N66 max e e e min e e e N67 max e e e min e e e N70 max e e e min e e e N69 max e e e min e e e N70A max e e e min e e e N71 max e e e min e e e N72 max e e e min e e e N73 max e e e min e e e N74 max e e e min e e e N75 max e e e min e e e N76 max e e e min e e e N77 max e e e min e e e N78 max e e e min e e e N79 max e e e min e e e N80 max e e e min e e e N81 max e e min e e N82 max e e min e e N83 max e e min e e N84 max e e min e e N85 max e e min e e N86 max e e min e e N87 max e e min e e N88 max e e min e e N93 max e e e-3 4 RISA-3D Version [P:\...\...\...\...\...\RISA\ '-20.5x20.5 Christie Lite Truss test.r3d] Page 3

41 150 min e e e N94 max e e e min e e e N95 max e e e min e e e N96 max e e e min e e e N97 max e e e min e e e N98 max e e e min e e e N99 max e e e min e e e N100 max e e e min e e e N101 max e e e min e e e N102 max e e e min e e e N103 max e e e min e e e N105 max e e e min e e e N106 max e e e min e e e N107 max e e e min e e e N109 max e e e min e e e N110 max e e e min e e e N112 max e e e min e e e N113 max e e e min e e e N115 max e e e min e e e N116 max e e e min e e e N117 max e e e min e e e N118 max e e e min e e e N119 max e e e min e e e N120 max e e e min e e e N121 max e e e min e e e N122 max e e e min e e e N123 max e e e min e e e N124 max e e e min e e e N125 max e e e min e e e-3 6 RISA-3D Version [P:\...\...\...\...\...\RISA\ '-20.5x20.5 Christie Lite Truss test.r3d] Page 4

42 207 N126 max e e e min e e e N127 max e e e min e e e N129 max e e e min e e e N130 max e e e min e e e N131 max e e e min e e e N133 max e e e min e e e N134 max e e e min e e e N136 max e e e min e e e N137 max e e e min e e e N139 max e e e min e e e N140 max e e e min e e e N141 max e e e min e e e N142 max e e e min e e e N145 max e e e min e e e N146 max e e e min e e e N149 max e e e min e e e N150 max e e e min e e e N153 max e e e min e e e N154 max e e e min e e e N155 max e e e min e e e N156 max e e e min e e e N157 max e e e min e e e N158 max e e e min e e e N159 max e e e min e e e N160 max e e e min e e e N161 max e e e min e e e N162 max e e e min e e e N163 max e e e min e e e N164 max e e e-3 3 RISA-3D Version [P:\...\...\...\...\...\RISA\ '-20.5x20.5 Christie Lite Truss test.r3d] Page 5

Failure in Flexure. Introduction to Steel Design, Tensile Steel Members Modes of Failure & Effective Areas

Failure in Flexure. Introduction to Steel Design, Tensile Steel Members Modes of Failure & Effective Areas Introduction to Steel Design, Tensile Steel Members Modes of Failure & Effective Areas MORGAN STATE UNIVERSITY SCHOOL OF ARCHITECTURE AND PLANNING LECTURE VIII Dr. Jason E. Charalambides Failure in Flexure!