Section Downloads. Design Process. Design Principles Outline. Basic Design Principles. Design Process. Section 06: Design Principles.

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1 Section Downloads Section 06: Design Principles 1 Download & Print TTT I Sec 06 Slides TTT I Sec 06 Handout Section 05 Truss Materials Design Values PS 20 Section 01 TPI Selection Repetitive Member Increase Version Design Principles Outline Design Process Design Process Basic Design Principles Statics Forces Moments Static Equilibrium Mechanics of Materials The two functions of the structural design process: Load Resistance LOAD RESISTANE or in other terms ATUAL ALLOWABLE # 2000# Factor of Safety = 2 4 Design Process Basic Design Principles Section 06 - Resistance Section 07 - Load 3 basic principles in the design of metal plate connected wood trusses: Statics Section 06 Mechanics of Materials Triangulation Section SBA 1

2 Statics Statics bodies at rest Equilibrium of bodies subjected to the action of forces Dynamics bodies in motion The following 3 concepts are used to statically analyze a structure: Forces Moments Static Equilibrium Forces Externally applied loads become internal forces 7 8 Axial Forces Act through the length of the truss member Inward or pushing force is axial compression Outward or pulling force is axial tension Transverse Forces Act perpendicular to the length of the truss member ause bending & shear stresses 9 10 Internal Forces Internal Tension & ompression Forces Neutral Axis Occurs at some depth in the beam where there is neither tension nor compression Unloaded Beam Beam with Point Load (Exaggerated Bending) ompression Tension Each Beam Element is Distorting Under Internal Forces SBA 2

3 Parallel Truss hord Axial Forces Pitched Truss hord Axial Forces T T T T T T T T T T T T T Howe Axial Forces Truss Tension (T) and ompression () acting at each joint Stress Reversals Truss Action Under Gravity Load Movement 15 Image ourtesy of Alpine Engineered Products 16 ompression Buckling Stabilize the column to increasing compression load capacity by 4x Incorrect Bracing Top chord buckling under its own weight Lateral Bracing to Prevent ompression Instability Section 08 Truss Design, Manufacture & Installation Overview SBA 3

4 Incorrect Bracing Permanent Web Bracing Broken webs that buckled too far out of plane Permanent Web Bracing Truss Design Drawing shows if permanent LR is required on a web LB Section 03 Design Responsibilities 19 All lateral braces require diagonal braces for stability 20 Permanent Web Bracing Purlins Diagonal Bracing Diagonal Bracing Top hord ontinuous Lateral Brace 21 4 ft. on-center 22 Moments Moment Equation P P Length (ft) Force (lbs) Force that produces a rotation of a member & subsequent bending stresses a L a L a Torque /Bending Moment = Forces that act a distance away to produce rotation about a point SBA 4

5 Moment Equilibrium Truss Bending Moments P L Rotation Point Rotation Point M wall = M end of board Static Equilibrium Static Equilibrium + positive direction of force L/2 L/2 negative direction of force Sign onvention can be reversed...just need to be consistent To achieve static equilibrium: the sum of all forces = zero ΣForces = 0 27 Sigma is the sum of 28 Static Equilibrium R 1 -R 2 = 0 R 1 + R 2 = 2000 lbs. R 1 = R 2 R 1 = 2000 lbs./2 = 1000 lbs. R 2 = 1000 lbs. ΣForces = 0 ΣV = 0 Set unknown values = known values Equations of Equilibrium Vertical Forces: ΣV = 0 Horizontal Forces: ΣH = 0 Moments: ΣM = 0 + positive direction of force negative direction of force SBA 5

6 Vertical Forces: ΣV = 0 ΣV = 0: P + w R 1 R 2 = 0 + positive direction of force negative direction of force Horizontal Forces: ΣH = 0 ΣH = 0: W R 1 R 2 = 0 Environmental Loads Generated by Truss-to- Bearing onnection Moments: ΣM = 0 Sign onvention Review ΣM RP = 0: (P x 2L) (2P x L) = 0 2PL 2PL = 0 0 = 0 Fulcrum [Rotation Point (RP)] + clockwise rotation - counter clockwise rotation ΣV = 0 ΣH = 0 ΣM = 0 + positive direction of force negative direction of force + clockwise rotation - counter clockwise rotation Free Body Diagrams Account for all forces acting on a structure Quiz SBA 6

7 Mechanics of Materials Strength of material Focused on lumber Lumber is anisotropic Wood ells Like drinking straws Stronger lengthwise than crosswise Section 05 Truss Materials rushing Six Lumber Design Values (see design values download page 3 Example 2x4 No. 1 SP) ompression Perpendicular to Grain ompression Parallel to Grain 565 psi 1650 psi 39 F b Bending Stress F t Tension Parallel to Grain F v Shear Stress F c ompression Perpendicular to Grain F c ompression Parallel to Grain E Modulus of Elasticity (MOE) 40 Lumber Design Values Using the Lumber Guides Southern Pine Use Guide Southern Pine ouncil Western Lumber Product Use Manual Western Wood Products Association The U.S. Span Book for Major Lumber Species anadian Wood ouncil Design Values Handout Section 02 Terminology SBA 7

8 Bending Stress (F b ) Tension Stress (F t ) Shear Stress (F v ) ompression Stress Perpendicular to Grain (F c ) Horizontal shear ompression Stress Parallel to Grain (F c ) Stress Stress = Force/Area w in. l in. P lbs. Area (A) = l" x w" = lw in 2 Stress (F) = Force (P) / Area (A) psi SBA 8

9 Stress TTT 1 Sec 06 Handout F c = Stress = Axial ompression Force (lbs.) (1.5 in. x 3.5 in.) Stress Example Stress Example P = 4000 lbs. axial tension force in a 2x4 chord A = cross-sectional area of the chord: A = (1.5 in.) x (3.5 in.) = 5.25 in. 2 Stress (F) in chord: F = P/A F = (4000 lbs.)/(5.25 in. 2 ) F = lbs./in. 2 F = 762 psi F t = 762 psi (actual stress) F c = P A Actual Allowable Stress Example ombined Stress Index (SI) Summation of axial & bending stresses divided by their respective allowable stress for a specific truss member. No transverse loads Select Structural SI = F t (actual) F b (actual) + = F t (allowable) F b (allowable) 762 psi 900 psi = Section 02 Terminology SBA 9

10 Stress Repetitive Member Factor Pressure and Stress Repetitive Member Factor 15% increase for bending stress Modulus of Elasticity E = Measure of material stiffness or how it will deform under load Selections from ANSI/TPI The higher the E value...the stiffer the material Section 05 Truss Materials E value does not correlate to strength. 58 Feedback Quiz SBA 10