This exercise involves the use of Space Gass to investigate several issues of a structural nature. The objective of this exercise is to enhance your understanding of structural behaviour, as well as develop a basic competency in the use of an industry-standard structural analysis computer program. This assignment consists of two parts.
Please note that you need to upload 2 files in the Moodle submission link by the due date:
1) Complete report file for parts A and B (in Pdf format);
2) The SPACE GASS file for Part B (in .SG format).
The following issues will be considered in arriving at the final mark:
Neatness of presentation of the written/typed work and quality of diagrams
Correctness of manual calculations, computer modelling and output results
The extent to which all appropriate calculations, diagrams, etc, are shown and the instructions given in the assignment brief are followed.
Readability and scale of the diagrams (i.e. printed from SPACE GASS).
Part a: 2-Span Continuous Beam
A 2-span continuous beam has the support arrangement, member sizes and loading shown
Each group will use an exclusive set of parameters for the input parameters. The method to generate input parameters is as follows: Count the number of letters of the first name of each group member and use the average of the two numbers as the value of X, then generate the parameters according to the table below (e.g. for Jack and Claire, X=5). Round up the obtained values to 1 decimal places.
a) Use the Slope-Deflection Method to analyse this beam and determine the joint moments MA, MB and MC. (Note: Please clearly identify the X value and the input you have used.) Note that the beams are bending about their strong axis (i.e. ‘x’ axis).
b) Using the joint moments determined in a), determine the vertical reactions VA, VB and VC. Thus draw the shear force diagram for this beam, determine from this the location of the maximum sagging bending moment in each span, and calculate the values of these maximum sagging bending moments. Finally, manually draw the full bending moment diagram for the beam.
Use Space Gass to analyse the beam to determine:
The full B.M.D. and compare the bending moments MA, MB and MC, and the maximum sagging B.M.’s with those determined in a) and b).
The maximum deflection in each span
d) Perform several checks of the output results from Space Gass in order to validate the correctness of these results. Note that the results of the slope-deflection analysis are not to be regarded as one of these checks. Treat this part as if the slope-deflection analysis had not been done. All calculations must be shown.
Part b: Portal Frame Model
This exercise continues on the second part of Assignment 1 to apply the wind loading on a typical steel portal frame building, using the SPACE GASS program. You need to use the group inputs and results of your calculations from Assignment 1. Please make sure you correct any mistakes undertaken in the previous assignment in order to get full marks for this part and mention a small summary of changes.
The diagram of the portal frame is attached. The portal frames are pinned-base, with the usual rigid connections at the eaves and the ridge. There is no haunch in the structure.
In a normal portal frame building design, a substantial number of wind loading scenarios would be considered. For this exercise, however, a very small subset of load cases, considering only the case of maximum uplift, will be investigated.
For the portal framed structure described above and in the attached diagrams, and based on the dead load + wind load cases described below, the following is required:
A)Determine the following maximum design actions, derived from Load Cases 4 and 5, for the first internal portal frame in from the end of the building:
• Maximum uplift on the footing (kN);
• Maximum hogging moment at the ridge (kNm);
• Maximum sagging moment at the rafter-column connection (kNm).
In addition to these answers, the following is to be included in the submission
All calculations involved in determining the loadings (from Assignment 1);
A fully dimensioned diagram of the model, showing member and node numbering and section sizes;
Fully detailed diagrams showing the loadings used for the three load cases LC1, LC2 and LC3;
The bending moment diagrams determined for the two load cases LC4 and LC5.
Note that the various diagrams should be produced by SPACE GASS.
B) Undertake a manual check of the column base vertical reactions for the two load cases LC4 and LC5. You should be able to get the same answer for the total nett vertical loading on the building as yielded by the sum of the two base reactions given by the SPACE GASS analysis. This provides a check that the loads have been correctly input into SPACE GASS.
i) Load Cases to Analyse
The following load cases should be input into SPACE GASS:
LC 1: Un-factored DL
LC 2: The total UDL (kN/m) from both internal and external wind pressures, due to wind coming from direction ‘A’
LC 3: The total UDL (kN/m) from both internal and external wind pressures, due to wind coming from direction ‘B’
LC4: 0.9 x LC1 + LC2
LC5: 0.9 x LC1 + LC3
ii) The Dead Loading
The self weight of the portal frame is to be allowed for using SPACE GASS’s ‘Self Weight’ option.
The weight of the roof and wall sheeting, insulation, and purlins/girts may be allowed for by assuming an equivalent UDL of 0.15 kN/m2. This obviously needs to be converted into a UDL (kN/m) for input into Space Gass. (Note that both the roof and wall distributed dead loading should be input using the ‘Global Inclined’ axis system, both in the –Y direction, obviously.