Mechanics Lab & Problem Sheet 2: Structures ( )

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Todd Wheeler
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1 Mechanics Lab & Problem Sheet 2: Structures ( ) Name (please print): P/1 Tutor (please print): Lab group Notes In the session you will be divided into small groups (about five per group). For the experiments you will be using small model structures mounted on a board. The structures can be loaded by hanging weights on different parts of the structure. The structures are simple, pin-jointed trusses, and one (or more) of the members can be replaced by a force meter to allow you to measure the force in that member. The force meters should be zeroed before adding the load. The force meters are designed so that they can measure tension and compression - remember to note which type of force it is. Once you have made a measurement, the structure can be partly disassembled and the force meter moved to a new position and the experiment repeated. ontinue moving the force meter around the structure until you have found the force in each member. e careful when dismantling the trusses, especially the connections with the force meters. Use black connectors where three members meet, white for four and use the short threaded lengths of tube with nuts at each end for more than four. fter the laboratory session, complete the problems at the end of the booklet (which include calculations for the structures in the laboratory experiments). Space has been left on some of the sheets for your working - use the blank facing pages if you run out of space on the main sheets. For the final questions you will need to use extra sheets for working, please staple them to the back of the booklet.

2 Structure 1 force meter X Y The structure is supported at each end. It is arranged so that a load (weight) can be put in one of two positions: X - symmetric load Y - asymmetric load Keeping the force meter in one place, apply a 150g load to the position X and then to position Y. Record your results on the diagrams below, remembering to note whether the force is compression or tension. Move the force meter to a new position and repeat. (You can make use of symmetries to reduce the number of moves.) Tension ompression m = = m g = m = = m g =

3 Structures 2a and 2b 2a) force meter These two similar structures differ only in the position of the diagonal members. They are supported at the top-left and top-right, and loaded with three equal masses (simultaneously). There are two types of members made up with force meters: one for the diagonals and one for all the other members. You can make use of symmetry to reduce the amount of moving of force meters you have to do. Remember to record whether the member is in tension or compression. 2b) Tension ompression

4 Structure Problems 1) The simple truss shown is supported by a roller at, a pin at and has a 150 gram mass applied at. hat is magnitude of the force acting at? Force acting at = N 150 g omplete the free body diagram above by adding all the external forces acting on the truss. rite down equations for (i) the sum of the horizontal forces acting on the truss, (ii) the sum of vertical forces acting on the truss and (iii) the sum of the moments of the external forces about the point. Thus calculate all the external forces acting on the truss. Mark the external forces on the diagram below.

5 Joint ssume the members meeting at point are under compression, complete the sketch of the forces acting on joint, marking on angles and known values. Sum the vertical components of the forces acting on to find the value of. = N Then sum the horizontal components of the forces acting on to find. (Hint: if the value is negative then the member is under tension, not compression). = N ecause the truss and loading are symmetric, the force in will be the same as in, and the force in the same as in. Mark all the known forces on the diagram at the bottom of the previous page, using the convention that a compressive force is marked by tension by. Joint Now sketch the forces acting on joint. Sum the vertical components to find the force in the member, then the horizontal components to find the force in the member. gain the force in must be the same as the force in. Mark all the forces on the diagram on the previous page. Joint (heck) heck that the sum of the horizontal forces acting on is equal to zero, and check that sum of the vertical forces acting on is zero.

6 For the following simple trusses, use the same procedure (with clearly laid out working) as in question 1 to find the external forces and all the forces in the members of each truss. ll the working should be done on separate sheets stapled to the back of this booklet but please put your final answers on the diagrams on the next page (external forces and forces in the members). Remember to check calculations where possible. 2) Unlike question 1, the loading isn't symmetric, so you will have to go through each joint. 150 g 3) Treat the truss as pinned at joint, with a vertical cable at, and ram weights at each of, and F. You can use symmetry to simplify some of the calculations. F 4) Similar to (3), but with the diagonal members in the other direction. omment on the differences between this truss and the truss in (3). F

7 nswers 2) 3) 4) omment:

Calculating Truss Forces Unit 2 Lesson 2.1 Statics

Calculating Truss Forces Unit 2 Lesson 2.1 Statics alculating Truss Forces alculating Truss Forces Principles of Engineering 22 Forces ompression body being squeezed Tension body being stretched Truss truss is composed of slender members joined together