Part IA Structural Design Course 2009/10 Handout 1 Supplementary Info to the DESIGN HANDOUT Supervisor version Text and pictures in grey are omitted from the student version. Fehmi Cirak, February 24, 2010
2 Part IA Structural Design Course 2009/10 Demonstrators: Dr Fehmi Cirak (fc286@cam.ac.uk) Alex Macdonald (adm59@cam.ac.uk) Problem: Aluminium Truss Bridge o Copy here problem description from Cam s handout. A highvoltage power mast as a sample of a truss structure. Tasks 1. As a pair design an aluminium bridge structure to carry a specified load without failure 2. Produce detailed manufacturing drawings 3. Build the structure in the workshop 4. Perform a cost analysis 5. Test the truss to destruction 6. Write an individual report Prizes available for the best projects
Project Timetable Session 1: Handout 1. Supplementary Info to the DESIGN HANDOUT 3 Thursday, 22 October (11am 1pm) Project briefing Tour of the test rig (Structures Teaching Lab) Tutorial on member sizing and stability Work on design concepts Session 2: Thursday, 29 October (11am 1pm) Tutorial on detailed joint design Tour of the workshops Work on detailed design and calculations Session 3: Thursday, 5 November (11am 1pm) Briefing on manufacturing drawings Finish detailed design and calculations Work on manufacturing drawings Session 4: Thursday, 12 November (11am 1pm) Finish manufacturing drawings Deadline for drawings: 5pm Monday 16 November Put here a deadlines section from Cam s notes. Todo
4 Part IA Structural Design Course 2009/10 Design Documentation Lab books: 1. All notes, sketches and calculations should be located at one end of the lab book (no loose sheets) 2. All working should be tidy and legible with the design process clearly laid out 3. The final report should be written at the other end of the lab book 4. Word processing is permitted for the text (pasted into the lab book) but not for calculations 5. All sketches, detailed drawings, component selection and calculations should be carried out by hand (no spreadsheets, CAD etc) Detailed manufacturing drawings Use A3 size paper and drawing boards provided (More details will be provided later.) o Don t go over Cam s notes. read it. Just mention that they are required to
Part IA Structural Design Course 2009/10 Handout 2 Member Sizing: Tension and Compression Supervisor version Text and pictures in grey are omitted from the student version. Fehmi Cirak, February 24, 2010
6 Part IA Structural Design Course 2009/10 2.1 Introduction: Truss Structures Truss structures provide a mass-efficient means of supporting loads. A carefully designed truss provides a stiff, strong structure with minimum material usage. Common examples include bridges, tower cranes, and roof structures. A truss structure carries the external loads through axial stresses in the members. The stresses may be in tensile (stretching) or compressive (pushing). Techniques for calculating these bar forces are presented in IA Structural Mechanics lectures. This handout will provide a guide for the selection of truss members to carry the required loads without failure. We will consider the stability of 2- and 3-dimensional frames, failure modes for bars in tension and finally failure in compression. 2.1.1 Revision of bar force calculations for a 2D pin-jointed planar truss Joint A: Joint B:
Handout 2. Member Sizing: Tension and Compression 7 2.2 Stability of the truss In devising a truss configuration, a triangulated arrangement of bars must connect load to the supports. Otherwise, the structure can fail as a mechanism under small loads: lengthens shortens The distance between the corner points can freely increase or decrease, if the joints are assumed to behave as pins. Accordingly, the triangulating bar is either in tension or in compression, in order to resist these changes in length: tension is preferable since compressive members are generally weaker due to buckling - see later. tension compression A single, vertical plane structures will normally move out of plane under very small vertical loads. For out-of-plane stability, the structure must be either truly 3-dimensional or two 2-dimensional planes connected together, For the latter, two aspects must be considered 1. The two planar trusses should be joined by perpendicular bars or ties at the corner points. 2. All planes on the outside of the new structure, which are potentially mechanisms, need to be triangulated using bracing.
8 Part IA Structural Design Course 2009/10 tie/spreader bar bracing The bracing is so-called because it carries no load, theoretically, since there is no component of load acting within each plane of triangulation. The loading plate (the point of application of the external load) may also tie the planes together. 2.3 Failure of bars in tension The strength of a bar in tension is dependent on the material behaviour. The stress versus strain for a ductile material such as mild steel in tension is as follows: σ σ elastic limit ACTUAL σ y IDEALISED ε ε If the bar stresses exceed the elastic limit, i.e. experiences yielding, further stress increments can result in large increments in strain. The behaviour is simplified by means of an idealised form (elastically-ideally plastic), with a distinct yield stress, σ Y σ y = 255 N mm 2 If the stress is uniformly carried over the cross-section, then its required cross-sectional area to avoid failure is A > bar force σ y In practice, end effects arise from the presence of a hole for connecting members by rivets or bolds. In the detailed computer simulation below, regions of practically zero stress are dark, and vice versa. Note also the high stresses behind the load at the hole.
Handout 2. Member Sizing: Tension and Compression 9 SECTION POINT 1 MISES VALUE +4.60E-01 +3.26E+03 +6.51E+03 +9.77E+03 +1.30E+04 +1.63E+04 +1.95E+04 +2.28E+04 +2.60E+04 +2.93E+04 +3.26E+04 +3.58E+04 +3.91E+04 +4.23E+04 LOAD FIXED KAS/2001 A smaller cross-sectional area is available near the hole to carry the bar force; consequently, the stresses here must locally increase, and this is therefore the most critical part under tension. The following effective area is therefore used: b 2 b D t b effective area For b >> t: A eff = 2bt }{{} total Dt }{{} hole bt }{{} 2 ineffective We therefore require: actual stress = bar force A eff < σ y 2.4 Failure of bars in compression If the member is very short and stocky, it fails by yielding when the stress in the bar reaches σ y. Otherwise, for slender bars, it fails by buckling, a geometric effect. The critical buckling force depends on: 1. The full cross-sectional area (end effects are not crucial) 2. The longest unsupported length between a pair of joints or connected points in a given member
10 Part IA Structural Design Course 2009/10 3. The cross-sectional shape Buckling design curves are provided in the Design Handout, and indicate the critical buckling stress, σ cr, for a given slenderness ratio L/b. For a single member, or a double back-toback but unconnected member, the (weakest) buckling direction is at 45 0, as shown. This is denoted as buckling in mode A: ACTUAL 45 angle REPRESENTATION buckling direction 45 single plane of buckling double (unconnected) Double members, connected together periodically along their length by rivets (or, bolts), behave differently: plane of buckling rivet mode B mode C (mode B prevented) Example: determine σ cr for L/b = 20 using the design curves below for aluminum.
Handout 2. Member Sizing: Tension and Compression 11 Buckling of Angle Struts: Aluminium Alloy 6082-T6 250 mode A mode B b b 200 b b mode C b σcr [N mm 2 ] 150 C 100 B A 50 0 0 10 20 30 40 L b Bracing members are used to reduce unsupported length L and, hence, the slenderness L/b in order to increase σ cr. tension brace l compression buckled l 2 (=L) As with stability, the bracing member nominally caries no force, and the smallest available section can be used.
12 Part IA Structural Design Course 2009/10 Worked example: using 16 16 mm angle (area = 58.7 mm 2 ), design a safe section for the following compression bar using the previous buckling curves for aluminium angle struts. 1. For a single section (which would buckle in mode A): Actual stress σ = 15000 58.7 = 255 N mm 2 Slenderness L b = 400 16 = 25 Mode A buckling gives σ cr = 43.0 N mm 2 σ > σ cr unsafe 2. For a double unconnected section which performs as two mode A bars Actual stress σ = 15000 2 58.7 = 127.5 N mm 2 L/b remains the same, as does σ cr = 43 N mm 2 σ > σ cr unsafe 3. Rivet the section in (2) along the length with several (e.g., three) rivets: performs as mode B with L = 0.4 m Mode B buckling gives σ cr = 97 N mm 2 σ > σ cr unsafe 4. Add a central bracing member to (3) to invoke mode B buckling over half its length Slenderness L b = 200 16 = 12.5
Handout 2. Member Sizing: Tension and Compression 13 Mode B buckling gives σ cr = 212 N mm 2 σ = 127.5 < σ cr = 212 safe
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Part IA Structural Design Course 2009/10 Handout 3 Joint Design Supervisor version Text and pictures in grey are omitted from the student version. Fehmi Cirak, February 24, 2010
16 Part IA Structural Design Course 2009/10 3.1 Introduction This handout will provide a guide for joint design and dimensioning. Poorly designed joints can compromise the load carrying capacity of the entire structure. For example, the I-35W Mississippi River bridge in Minneapolis collapsed on August 1, 2007 because of underdimensioned joints. The collapse killed thirteen people and injured 145 people. 3.2 Joints and Load Paths T T T For joint design it is helpful to think about load paths It is evident that every component on the load path must be capable transmitting load. The weakest component on the load path determines the overall strength. (Strength of a chain is determined by its weakest link.) The line of action is the line along the centroid of a cross-section.
Handout 3. Joint Design 17 The force in the member acts along the line of action. It is important to ensure that the lines of action are coincident at joints. 3.3 Failure Mechanisms of Joints 3.3.1 Member Failure Tension failure Tension failure has already been covered in Section 2.3. The reduced effective cross section A eff was introduced in order to take care of end effects. T max = A eff σ y Shear off failure Shear failure can be avoided by ensuring L > 3D, where D is the hole diameter.
18 Part IA Structural Design Course 2009/10 Bearing failure of member Bearing failure can be avoided by ensuring T max = σ y D t where D is the hole diameter and t is the profile thickness. 3.3.2 Rivet/Bolt failure Shear forces carried by rivets and bolts are tabulated on page 4 of the handout. Single shear In single shear, the joint rotates due to non-axis aligned member forces, which leads to tension forces in the bolt or rivet. Since rivets cannot carry tension forces do not use rivets in single shear. Double shear 3.3.3 Gusset plate The bearing force is tabulated on page 4 of the handout, as a function of sheet thickness and diameter D of the hole.
Handout 3. Joint Design 19 Bearing failure Plate buckling Note that unsupported sheet in compression may buckle. Therefore, compression members should be always abutted. 3.4 Summary Three crucial points to consider when designing joints are: Ensure that the lines of action of all the members intersect at a point Place all rivets / bolts on the line of action of the force (as far as possible) Check the capacity of every component of the joint (all members, all connectors, all gusset plates) Remember to avoid joints as much as possible by choosing designs with many continuous members.
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Part IA Structural Design Course 2009/10 Handout 4 Design Drawings and Final Report Supervisor version Text and pictures in grey are omitted from the student version. Fehmi Cirak, February 24, 2010
22 Part IA Structural Design Course 2009/10 Detailed Design Drawings In pencil, on A3 cartridge paper (provided) Do not remove drawing boards or drawing equipment: LR3A may be used weekday afternoons, DPO at the weekend. DPO should not be used for structural design during week The drawing must contain enough information for someone else to build the structure draw to scale mark all dimensions explicitly but don t include redundant information use a consistent projection include all relevant detail (fastener locations, orientation of angle sections, size and shape of gusset plates etc.) show as many views as are necessary
Handout 4. Design Drawings and Final Report 23 D etail A 3 S ide E levation E nd E levation P lan 115 G roup N o. : N ames: D ate: D rawn by: D rawing N o...of... T itle: G eneral A rrangement orj oint D etails 1 S cale: 1 :5 Sample drawing of general arrangement Sample drawing of a joint detail
24 Part IA Structural Design Course 2009/10 Test Session Tuesday, 1 December, 11am 1pm, Structures Teaching Lab 1. Bridges are tested to destruction, most expensive first 2. Test milestones: (a) does it fit the test rig? (b) does it reach the working load without noticeable deformation? (c) does it reach the failure load (= 2 working load)? (d) actual failure load? 3. Group presentation shared by both members: explain the merits of the design describe possible failure modes identify the critical failure mode 4. You may want to take photos before and after testing
Final Report Handout 4. Design Drawings and Final Report 25 1. Write the report at the opposite end of the lab book to your design notes 2. Text only may be word-processed and pasted in 3. Sketches, calculations and equations must be hand written 4. Include the following information (listed in Design Handout) summary (about 100 words) problem statement summary of the design process, including sketches detailed hand calculations for the final design costing sheet (completed after construction) differences: design versus as-built discussion on the test suggested improvements conclusions 5. Feedback session at the end of term