structural analysis homework solutions

structural analysis homework solutions

Structural Analysis Homework Solutions

1. Introduction

As we take a closer look at “Structural Analysis Homework Solutions”, let’s consider and appreciate the effort and ambition that had been achieved by arriving at the current higher level of understanding the behavior of structural members and its effect on the big picture, “Structure”, in general. The student is expected to take this course to have the ability to design and analyze any structural form and shape under a specific given set of loads (“Load” refers to the force, movement or any other actions that can act on the structure). At the beginning of any design, there were few major practical “steps” which need to be always followed by the designer. First, the load(s) that will be acting on the component in the structure must be identified. After that, based on the type of the structure (e.g beam, truss, frame, etc.), the internal forces that may occur in that particular structure have to be identified as well. This is what is called “Structural Analysis”. Last but not least, the type of material that is going to be used also must be considered when year, submitted. Then, an engineer or at least a student can produce a designed solution drawing based on the finding as a result through the first and second steps. Well, what can be expected is the designed solution will resist all the anticipated load; the ultimate internal load; and lastly, the external load (actual load). All the strategies used are all listed in the British Standard if it’s practiced under United Kingdom. Such a great matter, when all the effort has put in the mind and finally a specific work result has been found, we realized that . . what is next? Yes, it’s the excited moment where the final work in reality can start to be constructed based on the designed solution shown on the design drawing. Amazing, right?

2. Analysis of Beams

In order to obtain solutions related to problems in beam analysis, it is necessary to have an overall understanding of different beams and their supports. I would like to emphasize that in beam analysis, there are always vertical reaction forces at the supports, but there are no vertical forces in the beam itself, which should be kept in mind. For the second-degree equation of the deflection curve, given the value of y and the distance x from the origin point, the unknowns C1 and C2 can be obtained by solving the following two simultaneous equations. Thus, the deflection curve can be found. Welcome to the analysis textbook. For the beam problem, the bending moment at the X section, Mx, is the unknown. It is an essential procedure to calculate the bending moment at a specific point when we need to find out the exact value of Mx. There are mainly two theorems which can help find the bending moment before performing a detailed analysis. The first one is The Moment-Area Theorems, which consider the relations between a beam’s moment and the area of its loading. The second one is called the area-moment method, which is also used to analyze and find out the bending moment at a specific point. These theorems will be introduced in the next lecture. Shear forces should not be overlooked. It is essential to find the value of shear forces at different points, in particular, the maximum and minimum shear force. The obtained shear force should be used to perform a detailed analysis. In the slides, the methods to find the critical points and the maximum shear force will be introduced in detail.

3. Analysis of Trusses

Similar to the ladder given below, this truss is also analyzed for different loading conditions. We are considering a roof truss with a top joint supported. Only vertical members are used in this roof truss. Above is the internal load carrying capacities for different members according to the analysis done above. Shear forces are also analyzed for different segments, however only the maximum shear force is given. For the given sample data example, the longest segment is AB with a length of 1.8 m, so that length was taken for calculations. Three types of lines and also a symbol are used to represent the forces. Only the external forces are point forces. All members are connected with ball and socket joints. Joints can carry tension or compression, which is a major checking point in the truss analysis. When connecting members together, all members and joints are in a stable equilibrium when we come through creating each new member. For practical purposes, the analysis is carried out on the computer. However, the classical hand analysis with the help of Truss Analysis Software also produced similar results. All the internal forces in members are calculated at each stage. The questions we have in the Truss Analysis can be sub-categorized as shown below: Visualize Internal Member Forces, Calculate Internal Member Forces, Evaluate Internal Member Forces. Member Forces for Joint Gjug with Joint Load 2 kN in X Direction: This is a 3D diagram and forces are shown on members as tension or compression, in addition to the resultant load of the joint, J with 2kN in X direction. Up-to-date skills for engineers work efficiently. Creative Truss Analysis Sheet. The recurrence of the column members of the trusses in the middle and the edge gives a regular sequence. This requires a systematic approach. For the member forces in the edge, starting from maximum will always be in tension and f1 will be in compression.

4. Analysis of Frames

For the practical tasks in the labs, Simpson’s rule should be applied for finding the values of the terms of the stiffness matrix and it would bring the error of 0%. The steps to use the Simpson’s rule for practical labs’ homework or assignment are listed below. Could use either EA or 210EI as the modulus of the frame is constant. And then organise the areas. Then proceed to find Ax, Ay, L and the angle θ and LU. Afterwards, sinθ, cosθ and the rotational matrix L should be used to find A. With the previous steps, the first row of the stiffness matrix can be obtained. And similarly, for the second row of the stiffness matrix, the values can be found out by changing the values of Ax and Ay then the LU would be gained. Last but not least, perform and in order to make the obtained. G matrix become diagonal and eliminating the coupling effect, in order to calculate the final the answer (including RA, RB, fAx, fAy, fBy, fBx), the tension or compression of each member and also the warriors which has to be found. For the matrix to be totally diagonal, then the values of λ1 and λ2 can be found. Also the displacement can be found and then determined whether it is tensile or compressive forces.

5. Conclusion

To sum up, it is a very efficient way that we do not need to think much about the methods getting the member forces. We can just follow the four steps to get all the member forces and reactions from now on. However, we need to pay attention if there is any redundant, internal force caused by support settlement or beam deformation. We cannot ignore, for example, if some of the joints got no displacement at all. The structure will fail, and we cannot use the method for all the members. Also, it is very important for us to locate the external nodes before we start to locate the displacement node. If errors happen while in the process locating these nodes, the value of the displacements might give redundant results, or the whole structure failed as we calculate them. Since very small mistakes might lead to tragedy, it is very important to confirm the displacement nodes are located correctly. Appropriate command is also important and we must understand the physical meaning of the command. Otherwise, the structure will fail to analyze. I have learned so much in this chapter and these methods provided are extremely helpful in finding the solutions. I think this is very useful and professional. I hope that the materials we have learned here could help us more on our major study and future career life. Last but not least, I would like to take this opportunity to express my special thanks to our lecture, Dr. Narito and Mr. Ricky who taught me a lot throughout the whole lecture classes and individual online AutoCAD class. They are very responsible and willing to help if we are facing problems. I feel much appreciated of it. Thank you. I hope these solutions can help you guys.