Structural Analysis Scenario Objective of

Structural Analysis Scenario Objective of this project is to design an internal working structure a-B-C-D-E-F to support extractor fans as well as other equipment. The structure inside the building is a brickwork at 10 miles south of Derbyshire and Derbyshire. The proposed design is to extend beam AB and CD into the substantial bricks walls at a and D. Moreover, the BE and CF are to be located by pins at ground level.

The arrangement as well as associated loading is to be repeated at 10 m intervals indicated within the plan view. (Lightfoot, 1961). The project constructs a moment distribution table and determines the moments at the joints to an acceptable level of accuracy. Moment Distribution Table Moment distribution is an interactive method to solve an indeterminate structure. Moment distribution is also a mechanical process to deal with statically intermediary structure by the successive approximation within the moments in the structure. Typically, the moment distribution is a preferred calculation to reinforce a concrete structure.

(Volokh, 2002). To prepare the moment distribution table for this project, it is critical to analyze every joint of the structure to develop the fix-end moments. Analysis of the fixed-end moment of the project reveals that the fixed-end joints are not equilibrium. The goal of the project is to ensure that the fixed-end moments are released and the accuracy and equilibrium are achieved.

Thus, the moment distribution method is a process of solving the set of simultaneous equation using the iteration technique to arrive at the acceptable level of accuracy of the structure.

To apply moment distribution to make the joints to arrive at an acceptable level accuracy, the paper constructs Moment Distribution Table as being revealed in Table 1: Table 1: Moment Distribution Table I L (m) k=I/L D LL self w_u carry over 3309,519 3062,208 1880,912 947,9519 7885,906 11179,54 12314,61 13410,36 6161,137 -0,5 0 0 balance -3309,52 0 -2965,87 -1131,55 -3246,98 -7007,72 -14858,6 -12862,5 -10781,3 -3696,38 0,275671 0 carry over 0 -1482,94 -565,773 -1623,49 -3503,86 -7429,31 -6431,24 -5390,67 -1848,19 0,137836 0 0 balance 0 0 1229,225 875,7058 1884,615 4018,607 8765,949 5910,958 3987,674 1108,832 -0,07599 0 0 carry over 614,6127 437,8529 942,3074 2009,303 4382,974 2955,479 1993,837 554,4159 -0,038 0 0 0 balance -614,613 0 -828,096 -1180,64 -2349,55 -2697,33 -3130,14 -1274,13 -305,39 0,022798 0 0 0 carry over 218,9264 471,1537 1004,652 2191,487 1477,739 996,9184 277,208 -0,019 0 0 0 0 balance -218,926 0 -885,483 -1278,46 -1348,67 -909,588 -805,807 -138,594 0,010466 0 0 0 0 carry over -442,742 -639,228 -674,333 -454,794 -402,903 -69,2972 0,005233 0 0 0 0 0 balance 442,7416 0 788,1363 451,6507 315,2563 173,5627 43,82296 -0,00262 0 0 0 0 0 carry over 394,0681 225,8253 157,6282 86,78133 21,91148 -0,00131 0 0 0 0 0 0 balance -394,068 0 -230,072 -97,7638 -39,9513 -8,05333 0,000827 0 0 0 0 0 0 carry over -1150,36 -488,819 -199,756 -40,2666 0,004137 0 0 0 0 0 0 0 balance 1150,361 0 413,1452 96,00917 14,79893 -0,00152 0 0 0 0 0 0 0 carry over 206,5726 48,00458 7,399466 -0,00076 0 0 0 0 0 0 0 0 balance -206,573 0 -33,2424 -2,95948 0,000279 0 0 0 0 0 0 0 0 SUM 3535,136 -3535,14 5330,502 -3080,4 -3431,77 6508,857 18692,22 -2205,93 1664,013 -889,46 -13725,1 0,275671 0 Based on the moment distribution table, the paper presents bending moment diagram in the next section.

Bending Moment Diagram A Bending Moment Diagram (BMD) is an analytical tool used in conjunction with structural analysis to assist in the structural design. The bending moment diagram is achieved by determining the value of the bending moment and shear force at given moment. The paper has been able to determine the size and type of a member of a given material. More importantly, the bending moment diagram is used to determine the conjugation beam method or moment share method. (Caprani, 2008).

A Bending Moment Diagram is also used to create a moment variation with the length of the beam. The bending moment diagram is used to determine the deflection, shear stress as well as the slopes of the structure. The beam sign convention is as follows: A bending moment = M (x) A shear force =V (x). As being revealed in fig 1, the normal convention for a positive bending is designed in "U" form and spins clockwise to the left and spinning counterclockwise to the right.

Fig 1: Normal Bending Moment Convention Thus, the next step is to claculate the moment diagram. Calculation of Bending Moment Diagram This step determines the value of the moment, and the normal sign convention is used for the bending moment diagram and the functions are expanded to reveal the effects of each loading on the bending functions. The first step is to obtain the bending moment force equation to deterime support reaction. Determining support reactions: The beam has three reaction components and they are Ax, Ay, and Dy.

Applying the equation of static equilbrium, the value is FX = 0, Ax= 0 (eq. 1) F y = 0, Ay + Dy -180 x8-350=0 Ay +Dy= 1790 kN (eq. 2) Considering Z. axis that passes through and taking the moment of all the forces in the structure at z-axis i.e taking clockwise -- ve as well as anticlockwise +ve MZ= 0; Dy x 20- 350x180 -- 180 x 12x7 =0 (eq. 3) Solving eq.

3, we get 63000+ 15120 =78120/20=3906 kN Thus, Dy = 3906 kN Substituting the value of Dy in eq.2, we get Ay +Dy= 1790 kN Ay +3906= 1790 kN Ay= 1790-3906 Ay=-2116 kN Shear Force Calculation FA left = 0 FA left = -2116 kN FB = -2116 -160 x8=-3396 kN FC left = -3396 kN FC right = -2116- 1280+ 3906 kN =510 kN FD left=510 kN FD left=510-510=0 Bending Moment Calculation MA =0 MB = -2116x8 -160 x12x7= 3488 kN MC = -2116x20 -160 x12x19= -78800 kN Maximim bending +ve beding moment will be calculated using the property of similar triangles using shear force diagrams as follows: -2116 / x=-3396 / (8-x) -2116 / x=-3396 / (8-x) =13.24m Thus, the maximum +ve bending moment is 13.24m.

Mmax (+ve ) -2116 x 13.24 -180 x (13.24) x (13.24)/2= =43792.62 kNm Mmax (-ve) = -78800 kNm at point C Thus, the point at which the bendingis at 0 is calculated as follows: 3488/a=-78800/(8-a)= -0.36m Based on the moment bending diagram presented in Appendix 1, the paper discusses the appropriate factor of safety and the serial size of the structural section that should be used for beams, AB, BC and CD.

Safety Sized used for the Beam The goal of this project is to enhance appropriate safety of the structure capable of resisting the anticipated loading to enhance adequate margin of safety. Typically, the structure is designed to anticipate that the joints possess rotational stiffness to ensure that the moment around the frame and distribution of forces are not significantly different from the calculation. Elastic beam theory has been the basis of the structural steel design and analysis. Elastic beam theory is based on the steel structural element and analysis.

The elastic beam theory reveals that maximum load that a structure could be able to support is assumed to be equal with the load and this could cause a stress somewhere within the structure. This assumed to be equal with the stress Fy of the materials. For example, the members should be designed so that the computed bending stress for the load is not to exceed the yield stress. Engineers have generally used the elastic beam theory to design structure and achieve satisfactory results.

Elastic beam theory is an effective tool to enhance safety of the structure. It is essential to realize that non-application of elastic-beam theory in application of a structure could make a beam to deform under bending and shear. (Yaw. 2003). For example,.