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# Selecting Columns And Beams

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Selecting the correct column in order to support a given load without over engineering the situation takes in many factors. This section takes a step by step approach to one method of selection. The key terminology and calculations are explored by use of a simple example. Extracts of column tables are used to extract key variables. The tables used are extracted from standard construction engineering data sheets.

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### Selecting Columns And Beams

1. 1. Selecting Columns and Beams HNC In Engineering – Mechanical Science Edexcel HN Unit: Engineering Science (NQF L4) Author: Leicester College Date created: Date revised: 2009 Abstract: Selecting the correct column in order to support a given load without over engineering the situation takes in many factors. This section takes a step by step approach to one method of selection. The key terminology and calculations are explored by use of a simple example. Extracts of column tables are used to extract key variables. The tables used are extracted from standard construction engineering data sheets. © Leicester College 2009. This work is licensed under a Creative Commons Attribution 2.0 License .
2. 2. Contents <ul><li>Overview </li></ul><ul><li>Beams </li></ul><ul><li>Z – Modulus of Section </li></ul><ul><li>Columns </li></ul><ul><li>Effective Length </li></ul><ul><li>Selecting Columns and Beams </li></ul><ul><li>Selecting Columns </li></ul><ul><li>Selecting Columns – Example </li></ul><ul><li>Credits </li></ul>These files support the Edexcel HN unit – Design for Manufacture (NQF L4) For further information regarding unit outcomes go to Edexcel.org.uk/ HN/ Engineering / Specifications File Name Unit Outcome Key Words Stress introduction 1.1 Stress, strain, statics, young’s modulus BM, shear force diagrams 1.1 Shear force, bending moment, stress Selecting beams 1.2 Beams, columns, struts, slenderness ratio Torsion introduction 1.3 Torsion, stiffness, twisting Dynamics introduction 2.1/2.2 Linear motion, angular motion, energy, kinetic, potential, rotation
3. 3. <ul><li>When selecting the correct size beam for a particular situation the following must be taken into account; </li></ul><ul><ul><li>If the beam selected is to thin it will buckle under the applied loading </li></ul></ul><ul><ul><li>If the beam is to thick then there is a cost implication – we are spending more than we need to. </li></ul></ul><ul><li>It therefore follows that selecting the right section size for a particular application is important. </li></ul>Beams
4. 4. Z – Modulus of Section Max Bending Moment = And Z (section Modulus) = I / y max Different sections of beam have differing formulae for I Such that for a square section I = bd 3 12 And for a simply supported beam with a UDL over its full length M = wL 2 / 8 I  max y max
5. 5. Columns Columns are loaded by DIRECT COMPRESSIVE STRESS The two basic modes of failure are kneeing and buckling The critical buckling stress depends on the material concerned and how slender the column is. A measure of slenderness used is known as the SLENDERNESS RATIO SR = Effective length / Radius of gyration The effective L depends on how the beam is supported
6. 6. Effective Length <ul><li>Effective length – length between points at which the member bows out </li></ul><ul><li>For a pin ended member L e = L </li></ul><ul><li>Fixed ended member L e = 0.7 L </li></ul><ul><li>When one end is fixed L e = 0.85 L </li></ul><ul><li>(The other being pinned) </li></ul><ul><li>When one end is fixed and the other is free L e = 2 L </li></ul><ul><li>(such as a cantilever) </li></ul>
7. 7. Selecting Columns and Beams <ul><li>Beams </li></ul><ul><li>When selecting the correct size beam for a particular situation the following must be taken into account; </li></ul><ul><ul><li>If the beam selected is to thin it will buckle under the applied loading </li></ul></ul><ul><ul><li>If the beam is to thick then there is a cost implication – we are spending more than we need to. </li></ul></ul><ul><ul><li>It therefore follows that selecting the right section size for a particular application is important. </li></ul></ul>
8. 8. Selecting Columns <ul><ul><li>In order to select the correct column for a particular application </li></ul></ul><ul><li>Determine the effective length of the column required </li></ul><ul><li>Select a trial section </li></ul><ul><li>Using the radius of gyration value for this trial section calculate the slenderness ratio. </li></ul><ul><li>If the slenderness ratio is greater than 180, try a larger cross section trial section. </li></ul><ul><li>Using the slenderness ratio obtain the compressive strength from tables. (from the Y-Y axis) </li></ul>
9. 9. Selecting Columns - Example A column, pin ended, length 5m has an axial load of 1500kN. The steel has a yield stress of about 265MPa Effective L = 1 x 5 = 5m Choose a trial section – 203 x 203 / 86 From table 1 - Rad. Of Gyration = 5.32 SR = 5 / 0.0532(Needs to be in metre) = 94
10. 11. Extract from Table 2 Axis of Buckling – Y – Y Yield (MPa) SR = 94 Comp Strength = 200MPa (Approx) SRatio 265 275 340 25 258 267 328 50 221 228 275 75 187 192 221 100 138 141 153 150 74 74 77
11. 12. From Table 2 – Compressive strength is approx 150MPa The actual stress (  ) = Load / CSA = 1500 x 10 3 / 110.1 x 10 -4 = 132 MPa This value is 18MPa below the required stress value for this section We should now repeat the process until we have a stress value JUST below the 150 MPA value TRY IT YOURSELF