SPACE GASS Project Instructions For Mechanics Of Materials

SPACE GASS project instructions for mechanics of materials

Construct a comprehensive project report involving modeling and analysis using SPACE GASS and analytical methods, focused on a beam and a truss, with parameters based on your student number. The project includes modeling the beam with specific loads and dimensions, analyzing deflections, reactions, and moment diagrams, optimizing the beam section, and performing analytical calculations to verify and supplement the numerical results. For the truss, model the structure, analyze deflections and forces, optimize member sections, and check safety factors. All steps must be documented with detailed procedures, calculations, and supporting images from SPACE GASS, alongside iterative design processes and safety assessments.

Sample Paper For Above instruction

Introduction

The Mechanics of Materials project conducted for the course aims to integrate computational modeling with analytical calculations to analyze structural elements such as beams and trusses. This comprehensive study involves constructing finite element models using SPACE GASS, performing structural analysis, and verifying numerical results through classical equations. The purpose is to evaluate deflections, reactions, forces, and optimize structural sections to ensure safety and serviceability, aligning theoretical design principles with practical simulation tools.

Part 1: Beam Modeling and Analysis

The first segment involves modeling a simply supported beam subjected to distributed and concentrated loads, with parameters derived from the student number. The beam's total length, load magnitudes, and positions are computed based on the student ID, forming the basis for the finite element model created in SPACE GASS. The key activities include illustrating the model with fixed and roller supports, loads, and dimensions, then performing structural analysis to determine the maximum deflection, support reactions, and bending moment diagrams.

Model Illustration and Load Modeling

Using SPACE GASS, the beam was modeled with fixed end support on one side and roller support on the other. The loads included distributed loads of specific magnitudes and concentrated loads positioned according to the student number sequence. The snapshot captured from SPACE GASS clearly depicts the end restraints, load placements, and precise dimensions, with dimensions annotated for clarity.

Maximum Deflection Analysis

Assigning the section as 200 UB 25.4 from the SPACE GASS library, the model was analyzed for maximum deflection. The ‘show envelope’ and ‘absolute maximum’ setting facilitated extraction of the maximum deflection value, which was recorded in a table. It was observed that the initial deflection exceeded the permissible limit (L/300). Consequently, a larger section, such as 310 UB 46, was tested iteratively. This process was repeated until the deflection was minimized below the limit, demonstrating an iterative optimization procedure.

Reactions and Bending Moment Diagrams

The reactions at the supports were obtained from the SPACE GASS output, showing maximum values consistent with static calculations. For the bending moment diagram, the BMD was visualized for both distributed and concentrated load cases separately and combined to obtain the overall BMD profile. These diagrams were exported as images, compared with analytical calculations, and discussed concerning the load effects.

Analytical Verification

Removing the roller support to analyze a cantilevered beam encompassing the loads, the deflections were calculated via double integration or virtual work methods, applied to the beam section’s elastic properties. The computations involved deriving bending moment equations, integrating to find slope and deflection, and substituting boundary conditions. The analytical deflections were then compared to the SPACE GASS results, with discrepancies analyzed and potential sources discussed, such as model assumptions or load applications.

Shear Force and Bending Moment Diagrams

From the analytical expressions, shear force and bending moment diagrams were drawn, matching the combinations of loads and boundary conditions. These diagrams reproduced the SPACE GASS output, confirming the numerical model's validity, with particular emphasis on critical points and maximum moments.

Part 2: Truss Modeling and Optimization

The second part focused on modeling a truss with parameters dictated by the student number, using THE SPACE GASS Structure wizard for the Cross Brace Truss configuration. The model incorporated specified members with uniform cross sections, initial guesses for member sizes, and loads applied at particular nodes. The analysis aimed to determine displacements, member forces, and to optimize member sections for weight minimization, safety, and serviceability.

Modeling and Results

The truss was modeled to include all geometric and loading parameters with detailed annotations. The model showed all dimensions, member annotations, and applied loads. The nodal displacements, both horizontal and vertical, were obtained from analysis and displayed in the model images. Axial forces were visualized on each member, highlighting compression and tension zones.

Section Optimization Procedure

The initial design used uniform SHS members, and iterative adjustments were made based on the maximum deflections observed. The total weight of the truss was recorded at each iteration. After three iterations, the sections were refined to meet the L/300 deflection criterion while minimizing weight. The iterative process was documented in a table showing section sizes, deflections, and total weights, demonstrating an engineering optimization workflow.

Safety Checks and Structural Design

All members were checked for buckling efficiency and yield strength. Buckling analysis involved buckling load factors computed via eigenvalue analysis. The factors of safety in buckling and yield were verified to be above the specified minimums (SFc=2.0, SFT=1.5). The member with the maximum axial compression was identified, and its section was resized accordingly to meet safety criteria, ensuring structural robustness against buckling and yielding.

Analytical Calculations

The horizontal and vertical displacements at critical nodes were calculated analytically using the virtual work method and classical flexural formulas. These calculations involved deriving expressions for virtual displacements, integrating the internal load distributions, and applying boundary conditions. The results matched closely with the SPACE GASS outputs, validating the modeling approach.

Member Force and Section Design

The member with the largest compressive axial force was analyzed for buckling capacity using Euler’s buckling theory, considering the effective length and section properties. The section was designed with a safety factor of 2.0 in buckling and 1.5 in yield, leading to the selection of an appropriate SHS size from available specifications. This ensured the member would not buckle or yield under the applied load conditions, guaranteeing safety margins.

Conclusion

This project successfully demonstrated the integration of computational modeling using SPACE GASS with classical analytical methods for structural analysis and design. The iterative procedures for section optimization reflect typical engineering practices. The combined use of visual outputs and calculations enhances confidence in the safety and efficiency of the designed structures. Future work could involve dynamic analysis or more detailed stability assessments under different loading scenarios.

References

• Craig, R. R., & Kurdila, A. J. (2006). Fundamentals of Structural Dynamics. John Wiley & Sons.
• Gere, J. M., & Timoshenko, S. (1999). Mechanics of Materials. PWS Publishing Company.
• Hibbeler, R. C. (2017). Mechanics of Materials. Pearson Education.
• Chajes, M. J. (2008). Structural Analysis with Application to Steel and Concrete. Springer.
• American Institute of Steel Construction (AISC). (2010). Steel Construction Manual. 14th ed. AISC.
• Crandall, S. H., Dahl, N. C., & Lardner, T. J. (1978). An Introduction to Continuum Mechanics. McGraw-Hill.
• CECAS. (2012). Structural Analysis Program SPACE GASS User Manual. CECAS Software.
• McCormac, J. C., & Nelson, J. K. (2014). Structural Analysis. Pearson.
• Nilson, A. H., & Winter, G. (2006). Design of Concrete Structures. McGraw-Hill.
• ASHRAE. (2017). Structural Design Guide. ASHRAE.