Structures 1 Past Paper 2024 PDF

Structures 1 CIVL11001 & CIVL13001 & CIVL10031 1) Introduction This Course In this unit, we will look at some of the basics of structural mechanics. The concepts covered are fundamental to all future structures courses. They are also very powerful in themselves and used daily...

Structures 1 CIVL11001 & CIVL13001 & CIVL10031 1) Introduction This Course In this unit, we will look at some of the basics of structural mechanics. The concepts covered are fundamental to all future structures courses. They are also very powerful in themselves and used daily by practising engineers. With the knowledge gained in this course, you will be able to analyse, understand, and begin to design many types of structure, including the Eiffel Tower, cathedrals, aeroplane landing gear, and many aspects of the building you are in. Topics covered will include The philosophy and nature of structural engineering Equilibrium of rigid bodies (fundamental to all structural engineering) Analysis of trusses (such as used in football stadiums, bi-plane wings and many bridges). Material behaviour Analysis of forces and bending moments in rods and beams Deflections of beams Course Material These notes are intended to support the lectures, but they are not a replication of the lectures, so don’t expect Lecture 1 to correspond to Section 1 etc. The notes should be used in conjunction with the tutorial questions, examples, explanatory videos, lecture recordings/slides, other material on Blackboard and your own notes. If you understand all these learning materials and have understood and completed all the tutorial questions, you should do well in the assessments. However, if you want more detail or examples, or prefer a different style of presentation, there are many textbooks covering all aspects of the course available in the library and online (there are some recommendations on Blackboard). 2) Structures and Structural Engineering A structure is a solid body that carries loads (forces), either to the ground (such as a sky-scraper) or to another body (such as an aeroplane’s wing to the fuselage). The study of structures is a major branch of engineering that has applications in areas as diverse as the design of computer chips, hip- replacement joints, car-suspension systems and bridges. It features throughout the Civil, Mechanical and Aerospace engineering degrees at Manchester. There are various definitions of structural engineering from the serious and worthy to the more light-hearted (but actually very accurate): "Structural engineering is the art of moulding materials we don't wholly understand, into shapes we can't fully analyse, so as to withstand forces we can't really assess, in such a way that the community at large has no reason to suspect the extent of our ignorance."...James E. Amrhein (also attributed to others). *A significant part of these notes had been prepared by a previous lecturer for this unit, Dr Martin Gillie.  Put another way, structural engineering is concerned with ensuring the effect (E) of “actions” on a structure are less than its resistance (R) to those actions, or E 8 (try it!). Or, more simply, now take a “cut” a distance 𝑥𝑥 from the right-hand end of the beam as in Figure 25. Resolving forces vertically gives 𝑉𝑉 = −3𝑥𝑥 and taking moments about the cut gives 3𝑥𝑥 2 𝑀𝑀 = 2 The shear and bending moment given by these relationships is plotted in Figure 27 in green. Notice there is a step change in the shear force over B due to the point load effect of the support. This is not strictly accounted for by either expression for shear force above. Example 2 Question: Draw the bending moment and shear force diagrams for the beam in Figure 26 3kN/m 10kN 2m A B 3m 8m Figure 26 This is more complex than Example 1 but the same principles apply. Considering equilibrium of the whole beam gives RA=5.9kN and RB=8.6kN. Next we take a “cut” a distance 𝑥𝑥 from the left- Structures 1 (Aerospace, Civil, Mechanical) CIVL 11001 & 13001 & 10031 21  3kN/m A B C 9kN 27kN 15 Shear force (kN) 3m x -9 -12 Bending moment (kNm) 24 x -13.5 6m Figure 27 The solution to Example 1. It is normal to plot the SFD and BMD directly under a FBD of the beam being considered, as done here. Identifying all the key points on the diagrams, such as the locations and magnitudes of peak values is also good practice – this can be quite tricky for more complex problems. Red lines were calculated by taking a “cut” a distance x from the left-hand end of the beam; green lines by taking x from the right-hand end. hand support and obtain expressions for the shear force and bending moment along the length of the beam. Because there are two loads, one of which is continuous, three expressions will be needed, each valid for different values of 𝑥𝑥. Free-body diagrams for each case are given in Figure 28. Resolving forces vertically for the three cases gives expressions for the shear force in the beam (remember the area of a triangle is half base times height.) 1 𝑉𝑉 + 5.9 − 𝑥𝑥. 𝑥𝑥 = 0 for 𝑥𝑥