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Assessment questions 4 Objectives This assessment item relates to the course learning outcomes 1, 2, 3 and 4 Question 1 Topic: Section Properties: For the beam below (see dimensions below); (1) Calculate, dimension and sketch the location of the horizontal centroidal axis (2) Calculate the Second Moment of Area Ixx (horizontal axis only) (3) Calculate the Section Modulus Zxx (horizontal axis only) Make sure you show all calculations The dimensions for the beam are as follows: bf= 150mm (both flanges) d = 200 mm tf = 12 mm (both flanges) tw = 10 mm h = 176 mm Question 2 Topic: Analysis of statically determinate trusses The truss below has been designed to support a 60 kN load. Using the Method of Joints (1) Calculate both the horizontal and vertical reactions at A and E (2) Calculate the force in each member of the truss (3) Draw a truss diagram showing the force in each member and show which member is in tension or compression (4) Calculate the force in member BF using the method of sections Note: · For your calculations you can assume all truss members are pin connected · Ignore the self-weight of the truss. · Make sure you show all workings. Question 3 Topic: Beams- shear force and bending moment For the beam below; (1) Calculate the beam reactions at A and C. (2) Calculate the bending moment at A, B, C and D. (3) Draw shear force and bending moment diagrams for the beam and label values for the maximum shear force and bending moment - Show all workings. Question 4 Topic: Bending and shear stresses: The timber beam below spans 7.0m and carries a uniformly distributed load of 1.5 kN/m (including the self-weight of the beam). The beam is 75 mm wide and 240 mm deep. (1) Calculate the average vertical shear stress at; 1. x = 3.5m 2. x = 1.75m and 3. x = 0 (at the support) (2) Sketch the shear force diagram and indicate maximum and minimum values (3) Calculate the horizontal (longitudinal shear stress) at x = 1.75m at each of the following points of the section. 1. at the top surface 2. at 60mm and 3. at 120mm from the top 4. 180mm from the top (4) Sketch the internal horizontal shear stress distribution diagram where the maximum vertical shear stress is located. Indicate shear stress values. Page | 1 Page | 1 Page | 1 Module Title: Equilibrium and building structures 1 BLAR11032 Structural Forms & Analysis Updated: February 2020 Phillip Harrison MBA MFP BE (Civil) Dip Arch Topic Equilibrium and building structures 1–2 Learning outcome By successfully achieving the stated ‗enabling objectives‘ for this topic, you should be able to discuss with your work colleagues the concepts of equilibrium and the application of the idea of equilibrium in analysing the stability of objects in nature and in building. Enabling objectives You may be assessed on the following objectives. These objectives should enable you to achieve the learning outcome stated above. Understand the basics of forces on structures, how they are measured and what happens when there is more than one force Understand and do simple calculations involving ―forces‖ and ―moments‖ Describe and undertake calculations involving the laws of statics. Apply the 3 equations of equilibrium to given situations, that is: – the sum of the forces in the horizontal direction equals zero – the sum of the forces in the vertical direction equals zero – the sum of the moments about any point equals zero. Identify when forces are concurrent or non-concurrent Understand the difference between internal and external forces. What you will need Suggested study time 12 hours Resources Textbook—Wyatt, KJ & Hough, R 2013, Principles of structure, 5th edn, UNSW Press, Sydney. Chapter 1 Parts 1.1- 1.9 incl. Chapter 4 Graphical Statics Materials for Exercise 1–1: 6 plastic straws and 1 rubber band, 1 pillow or cushion. See Moodle topic for other resources Equilibrium and building structures 1–3 Introduction Have you ever tried to build a house of cards? Unless each card is placed carefully the structure falls down. It gets even more difficult as you build the card castle higher because the cards on top are relying on those below to support them. If you had the choice, would you build your card house on a smooth table or a table with a blanket over it? Why? In this first two weeks, we will be looking at some basic concepts in structural analysis: Equilibrium of structures, which explains why each card must be placed so carefully in the card house. Loads and load paths—the weight of each card at the top of the castle is a load that must be transferred down through the lower cards to the table top. Support conditions—it is easier to build a card house on a blanket than on a smooth table-top because the maximum possible horizontal reaction load is larger for the blanket. Mathematical skills This course has been written based on the assumption that you have basic mathematical skills in these areas: 1. Solving equations 2. Trigonometry 3. Vector operations. The following have been included to assist you if you need to revise these skills. Links are also available in Moodle topic tab to additional resources. Topic 1: Solving Equations http://en.wikipedia.org/wiki/Linear_equations http://www.youtube.com/watch?v=GmMX3-nTWbE http://www.idomaths.com/simeq.php Topic 2: Trigonometry Textbook Wyatt & Hough 2013, Appendix 1, pp. 191-193 Topic 3: Vector Operations Textbook Wyatt & Hough 2013, Appendix 1, pp. 194-199 and Chapter 4 http://www.youtube.com/watch?v=pimr9I92GZY IMPORTANT NOTE: If you believe you do not currently have the necessary mathematical skills to complete this unit, please contact your lecturer or course coordinator immediately to discuss your options. CQU has additional help available. http://en.wikipedia.org/wiki/Linear_equations http://www.youtube.com/watch?v=GmMX3-nTWbE http://www.idomaths.com/simeq.php http://www.youtube.com/watch?v=pimr9I92GZY Equilibrium and building structures 1–4 Forces Engineers, architects and builders have Sir Isaac Newton to thank for transforming building construction from a trial and error process into a mathematically reliable system that can accurately predict the behaviour of a structure. Understanding what forces are being applied on a structure is essential before we can begin to design a building or its elements. Buildings often fail because the designers did not consider all the possible forces or potential forces (e.g. The World Trade Centre in New York and the building collapses in Christchurch New Zealand). Therefore it is essential that all members of a construction team (not just the engineers) contribute to assessing what current and future forces the structure will be required to support. Activity: Review Newton‘s Laws on page 2 of the text. External Forces Engineers are very interested in forces and how they act on a structure. So what do we mean by a force? A force is an influence that tries to change a structure‘s (or its components) movement, direction or shape from its state at rest. A push or a pull is an example of a force. We will see that a force has both magnitude and direction and can be pictured as a vector to simplify our understanding. We measure forces in Newtons. What is a Newton of force? A force of one Newton applied to a mass of one kilogram (kg) will produce an acceleration of one meter per second squared (m/s 2 ). Can we picture what a Newton of force looks like? The acceleration we deal with is the earth‘s gravity which is why buildings tend to collapse downwards (on our planet). On the earth‘s surface a mass of 1 kg exerts a force of approximately 9.8N. So a mass of 1,000kg (about the weight of a small car) will exert a force of 9.8 x 1,000N or 9.8kN (kilonewton). In engineering our basic unit of force is the kilonewton or kN (1 kN = 10 3 N) Question: If you weight 70kg what force will you exert on the earth? Answer: 70kg x 9.8N = 686N = 0.686kN External forces are forces that are applied to a structural element. These external forces in turn will cause internal forces inside the element. These internal forces in turn create stresses and strains inside the material. What happens to these forces will depend on the nature of the material and its shape. Internal forces are very important forces and we will look at these later in the course. For now we will consider only external forces. A force has a magnitude (kN), a direction (with respect to some reference), and a location (the co- ordinates of a point through which the force passes). This is where ―vectors‖ are useful in picturing what is happening. Vectors are simply ways of representing forces in diagram form. Resultants and Components On most structures there is more than one force acting on body. We often wish to know the net effect of these separate forces. This is done by calculating one equivalent force sometime called the resultant of the forces. Look at figure 1.2 & 1.3 (refer to page 5 of the text) and you can see how this is achieved using vectors and basic trigonometry skills. If