Transcript Slide 1
Bridge Building Tips Overview Today’s discussion will cover; Column Strength Demonstration Strength of structural members Bridge Designer Program Features 2 Classification of loads How to calculate the strength of a member How to get information about your design Tips on improving your design How Strong is it? Strength is defined by how large a load (force) can be supported without damage. The strength of any member is determined by the maximum amount of stress it can withstand. The maximum stress that can be withstood depends on the material it is made of. How forces create stress depends on 3 Shape of the material Direction of the load Stress is a Vector Quantity, it has a Magnitude and a Direction Forces Create Stress 4 To determine the strength of something, we have to determine the relationship between forces and stress. Stress Stress is the amount of force applied to an area Can you hold a book and a pencil in the palm of your hand? Engineering Mechanics 5 Engineering Mechanics How about like this? The force is the same, but the stress is not Material Type 6 For engineering purposes, all solid materials behave like springs Engineers determine the strength of materials by testing them to measure their Modulus of Elasticity. We call this “E” The value E is a measure of how much a material will stretch when subjected to stress. This stretching is called Strain Measuring Material Strength Engineers measure the strength of a material by subjecting it to stress, and measuring how much it strains. Ultimate Strength Stress Elastic Strength Yield Stress E is the slope of the Stress/Strain curve 7 Ultimate Limit Elastic Limit Strain You can stretch the material in the elastic region, and it will return to it’s original position. Stress If you stretch it beyond the elastic limit, (yield stress) the material will be permanently deformed. At the Ultimate limit, it will break Strain 8 An member is “Damaged” when it's Yield Stress is exceeded (stretched past it’s elastic limit) Some Material Properties E (KN/m2) Steel 9 Yield Stress (KN/m2) Quenched & Tempered 2.0x108 485,000 High Strength, Low Alloy 2.0x108 345,000 Carbon Steel 2.0x108 250,000 Aluminum 6061-T6 0.69x108 275,000 Oak 0.17x108 31,650 Concrete 0.31x108 13,760 Loads Classification Tension Compression P 10 “P” = the applied load P The force on both columns is the same magnitude, but in different directions, so these columns will have different amounts of stress. Tensile Strength Strength of a member in tension is called it’s tensile strength. It is determined by the maximum stress the material can handle It does not depend on the material shape. 11 Stress = Force x Area Max. Allowable Force = Area / Yield Stress Cross Section Area Area of a solid bar Area of a hollow tube Under Tension, if the area of two members is the same, then the tensile strengths are the same 12 Compressive Strength 13 The Compressive strength of a column is influenced by it’s shape The maximum compression load a column can support without buckling is called the Critical Column Load P Critical Column Load Equation P crit P EI 2 Pcrit 2 L Material Shape 14 E = Modulus of Elasticity I = Moment of Inertia L = Column Length L Also called the Euler Buckling Load in honor of mathematician Leonhard Euler who was the first to person to solve this problem (1757) Moment of Inertia (I) 15 The parameter I is the Moment of Inertia (MOI). It relates the shape to the maximum stress Moment of inertia is calculated relative to some line of reference Sample MOI Calculations Y Y R X H X B IX 16 BH 12 3 IY HB 12 3 I X IY R4 4 Y Ho X HI For a hollow tube, subtract I of the inside from I of the outside I X I X O I XI BI Bo 17 BO H O3 BI H I3 12 For a square section, H = B Y Y X B Bo X BI B BI Bo I X IY B4 12 18 I X IY BO4 BI4 12 Y t For a square tube with constant wall thickness, t, the inside length is BI=BO-2t X B B I X IY BO4 BI4 12 19 B 4 B 2t 4 I X IY 12 Sample Calculation Consider the ¼ inch Oak Column E=0.17 x 108 I = (0.25)4 / 12 EI 2 Pcrit 2 L Pcrit = 17,385 / L2 (Newtons) Pcrit = 7,980 / L2 (Lbs) 20 (L in meters) (L in inches) P Sample Calculation 50 350.0 45 40 Yield Stress 300.0 35 250.0 30 Load (lbs) Load (lbs) Critical column load Vs. length for an Oak column 1/4” Square Column Buckling Column Buckling Load Load 200.0 25 20 150.0 15 100.0 10 50.0 5 0 10 21 0.0 120 14 5 16 18 10 20 1522 24 20 26 25 28 Length (in) (in) Length 30 30 32 35 34 36 40 West Point Bridge Designer Bridge Building Checklist Use the Symmetry Guides Reduce all members to minimum size 22 Use the member list Shorten long members that carry large compression loads Use the Cost Calulations report to reduce the number of different size members Experiment with different materials Experiment with different shapes (move joints) Vocabulary 23 Strength Tension Compression Stress Strain Elastic Strength Ultimate Strength Yield Stress Ultimate Stress Modulus of Elasticity (E) Moment of Inertia (I) Critical Column Load (Euler Buckling Load)