Reference no: EM132272727
COMPUTATIONAL MECHANICS
Assignment
The attached drawing shows details of one-half of a step ladder. This ladder consists of two 85 mm x 20 mm x 2 mm (thick) aluminium channel-section rails with 5 steps equally spaced at a vertical height of 300 mm. A 2 mm thick aluminium cap at the top of the ladder - see Section B in the drawing for details - provides the top step for this ladder. The main steps here are assumed to be constructed in two halves and pressed together to form the complete step. Each of these sections is manufactured from 1mm thick aluminium and, when pressed together to form the step, parts that touch together - the centre section and two end parts of the step (see drawing for details) - effectively form a 2mm thick section. The steps are connected to the rails using the two oval-shaped part of the step protruding through and held to the rails; see figure 1. For this assignment assume the aluminium has a yield strength to 300MPa. Note even though the ladder in this assignment is based on the geometry of a commercially available step ladder, several simplifications have been made so much so that the results from this model cannot be used to infer the mechanical strength of similar shaped commercially available ladders.
Figure 1. Ladder step connection to rails
In this assignment you are required to:
1. Create a beam finite element model of the ladder shown in the drawing. This will require you to build the step cross-section in Strand7 using the details supplied in the drawing. I suggest you save this plate cross-section of the step as a separate model as it will be useful in part 2 of the assignment.
2. Create a detailed plate finite element model of the step ladder. I suggest you start with the plate cross-section model of the step and use this geometry to define beams on the centreline of all parts of the step allowing you to create the plate model by extrusion. The difficult part in building this model is creating the plate finite element mesh at the intersection between the step and the rail. I suggest you build this mesh before extruding the beams on the cross-section to create a plate mesh of the step. I will discuss this part of the assignment in class.
3. For both models, create boundary conditions simulating the ladder leaning up against a wall with the rail making an angle of 70° to the horizontal (as per the drawing). Here prevent nodes "on the ground" from moving vertically and horizontally outwards and on the wall from moving horizontally. Note you need to prevent a sufficient number of nodes in the model from moving horizontally perpendicular to the outwards direction to prevent rigid body motion. Apply a vertical load equivalent to 120kg on the middle step simulating a person standing on the step. I will leave the method of applying this load in the beam and plate models up to you but you need to document your method in the report. For both models, determine the deflection and stress within the step- ladder under load. Compare predictions from the models and comment. You may want to look at predicted deflections and stresses, location of high stress points, deflected shape under loading, factor of safety determined from both models and predicted weight of both models (use the same grade of aluminium alloy in each model).
Report
Submit a report documenting all requested information outline above.