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Introduction to Structural Member Properties Structural Member Properties Moment of Inertia (I) is a mathematical property of a cross section (measured in inches4) that gives important information about how that crosssectional area is distributed about a centroidal axis. Stiffness of an object related to its shape In general, a higher moment of inertia produces a greater resistance to deformation. ©iStockphoto.com ©iStockphoto.com Moment of Inertia Principles Joist Plank Beam Material A Douglas Fir B Douglas Fir Length Width Height Area 8 ft 1 ½ in. 5 ½ in. 8 ¼ in.2 8 ft 5 ½ in. 1 ½ in. 8 ¼ in.2 Moment of Inertia Principles What distinguishes beam A from beam B? Will beam A or beam B have a greater resistance to bending, resulting in the least amount of deformation, if an identical load is applied to both beams at the same location? Moment of Inertia Principles Why did beam B have greater deformation than beam A? Difference in moment of inertia due to the orientation of the beam Calculating Moment of Inertia – Rectangles Calculating Moment of Inertia Calculate beam A moment of inertia = = = 1 .5 in . 5 .5 in . 3 12 1 .5 in . 1 66 .3 7 5 in . 12 249.5625 in. 12 = 21 in. 4 4 3 Calculating Moment of Inertia Calculate beam B moment of inertia = = = 5 .5 in . 1 .5 in . 3 12 5.5 in. 3.375 in. 12 1 8 .5 6 2 5 in . 12 = 1 .5 in . 4 4 3 Moment of Inertia 14Times Stiffer Beam A Beam B IA = 21 in. 4 IB = 1.5 in. 4 Moment of Inertia – Composite Shapes Why are composite shapes used in structural design? Non-Composite vs. Composite Beams Doing more with less Area = 8.00in.2 Area = 2.70in.2 Structural Member Properties Chemical Makeup Modulus of Elasticity (E) The ratio of the increment of some specified form of stress to the increment of some specified form of strain. Also known as coefficient of elasticity, elasticity modulus, elastic modulus. This defines the stiffness of an object related to material chemical properties. In general, a higher modulus of elasticity produces a greater resistance to deformation. Modulus of Elasticity Principles Beam Material Length Width Height Area I A Douglas Fir 8 ft 1 ½ in. 5 ½ in. 8 ¼ in.2 20.8 in.4 B ABS plastic 8 ft 1 ½ in. 5 ½ in. 8 ¼ in.2 20.8 in.4 Modulus of Elasticity Principles What distinguishes beam A from beam B? Will beam A or beam B have a greater resistance to bending, resulting in the least amount of deformation, if an identical load is applied to both beams at the same location? Modulus of Elasticity Principles Why did beam B have greater deformation than beam A? Difference in material modulus of elasticity – The ability of a material to deform and return to its original shape Characteristics of objects that affect deflection (ΔMAX) Applied force or load Length of span between supports Modulus of elasticity Moment of inertia Calculating Beam Deflection 3 ΔMAX = FL 48EI Beam Material Length (L) Moment Modulus of Force of Inertia Elasticity (F) (I) (E) A Douglas Fir 8.0 ft B ABS Plastic 8.0 ft 20.80 in.4 1,800,000 250 lbf psi 20.80 in.4 419,000 250 lbf psi Calculating Beam Deflection 3 ΔMAX = FL 48EI Calculate beam deflection for beam A ΔMAX = 2 5 0 lb f 9 6 in . 3 4 8 1 ,8 0 0 ,0 0 0 p si 2 0 .8 0in . 4 Δ M A X = 0 .1 2 in . Beam A Material Douglas Fir Length 8.0 ft I 20.80 in.4 E Load 1,800,000 250 lbf psi Calculating Beam Deflection 3 ΔMAX = FL 48EI Calculate beam deflection for beam B 3 ΔMAX = 2 5 0 lb f 9 6 in . 4 8 4 1 9 ,0 0 0 p si 2 0 .8 0 in . 4 Δ M A X = 0 .5 3 in . Beam B Material ABS Plastic Length I 8.0 ft 20.80 in.4 E 419,000 psi Load 250 lbf Douglas Fir vs. ABS Plastic 4.24 times less deflection Δ M A X A = 0 .1 2 in . Δ M A X B = 0 .5 3 in .