1. Structural Member Properties Moment of Inertia (I) is a mathematical property of a cross section (measured in inches 4 ) that gives important information about how that cross- sectional area is distributed about a centroidal axis. In general, a higher Moment of Inertia produces a greater resistance to deformation. Stiffness of an object related to its shape ©iStockphoto.com

2. Calculating Moment of Inertia - Rectangles Why did beam B have greater deformation than beam A? Moment of Inertia Principles Difference in Moment of Inertia due to the orientation of the beam

3. Calculating Moment of Inertia Calculate beam A Moment of Inertia

4. Moment of Inertia – Composite Shapes Why are composite shapes used in structural design?

5. Beam Deflection – Measurement of deformation – Importance of stiffness – Change in vertical position – Scalar value – Deflection formulas

6. Beam Structure Examples

7. What Causes Deflection? Snow Live Load Roof Materials, Structure Dead Load Walls, Floors, Materials, Structure Dead Load Occupants, Movable Fixtures, Furniture Live Load

8. Loading Snow Live Load Roof Materials, Structure Dead Load Walls, Floors, Materials, Structure Dead Load Occupants, Movable Fixtures, Furniture Live Load

9. Types of Loads

10. Factors that Affect Bending – Material Property – Physical Property – Supports

11. Physical Property - Geometry

12. Beam Supports

13. Beam Deflections Spring Board Deflection Bridge Deflection

14. Calculating Deflection on a Spring Diving Board Known: Pine (E) = 1.76 x 10 6 psi Applied Load (P)= 250 lb Pine Diving Board Dimensions: Base (B) = 12 in. Height (H) = 2 in. 72 in. P  Max ? 250 lb

15. Deflection of Cantilever Beam with Concentrated Load  max = P x L 3 3 x E x I Where:  max is the maximum deflection P is the applied load L is the length E is the elastic modulus I is the cross section moment of inertia P L  max

16. Moment of Inertia (MOI) Moment of Inertia (I) is a mathematical property of a cross section (measured in inches 4 ) that is concerned with a surface area and how that area is distributed about a centroidal axis.

17. Calculating Moment of Inertia (I) I = (12 in.)(2 in.) 3 12 I = (12 in.)(8 in. 3 ) 12 I = 96 in. 4 12 I = 8 in. 4

18. Cantilever Beam Load Example  max = P x L 3 3 x E x I  max = (250 lb) (72 in.) 3 (3) (1.76 x 10 6 psi) (8 in. 4 )  max = (250 lb) (373248 in. 3 ) (3) (1.76 x 10 6 psi) (8 in. 4 ) Known: Pine (E) = 1.76 x 10 6 psi Applied Load (P) = 250 lb 72 in. P  Max 250 lb

19. Cantilever Beam Load Example  max = (9.3312 x 10 7 lb)(in. 3 ) ( 5.28 x 10 6 psi)(8 in. 4 )  max = (9.3312 x 10 7 lb)(in. 3 ) (4.224 x 10 7 psi)(in. 4 )  max = (9.3312 x 10 7 ) (4.224 x 10 7 in.)  max = 2.21 inches

20. Calculating Deflection on a Pine Beam in a Structure Known: Pine (E) = 1.76x10 6 psi Applied Load (P)= 200 lb Beam Dimensions: Base (B) = 4 in. Height (H) = 6 in. Length (L) = 96 in. P L  max

21. Deflection of Simply Supported Beam with Concentrated Load  max = P x L 3 48 x E x I Note that the simply supported beam is pinned at one end. A roller support is provided at the other end. Where:  max is the maximum deflection P is the applied load L is the length E is the elastic modulus I is the cross section moment of inertia P L  max

22. Calculating Moment of Inertia (I) I = (4 in.)(6 in.) 3 12 I = (4 in.)(216 in. 3 ) 12 I = 864 in. 4 12 I = 72 in. 4

23. Simply Supported Beam Example  max = P x L 3 48 x E x I  max = (200 lb)(96 in.) 3 (48)(1.76x10 6 psi) (72 in. 4 )  max = (200 lb)(884736 in. 3 ) (48)(1.76x10 6 psi)(72 in. 4 ) Known: Pine (E) = 1.76x10 6 psi Applied Load (P) = 200 lb P 96 in.  max

24. Simply Supported Beam Example  max = (1.769472 x 10 8 lb)(in. 3 ) (8.448 x 10 7 psi)(72 in. 4 )  max = (1.769472 x 10 8 lb)(in. 3 ) (6.08256 x 10 9 psi)(in. 4 )  max = (1.769472 x 10 8 ) (6.08256 x 10 9 in.)  max = 0.029 inches