Design of a steel skew cantilever followed by construction and testing to destruction

Design of a steel skew cantilever followed by construction and testing to destruction. Analysis and improvements section included. Aiming for minimum weight and structural costs, while achieving a working load of 1kN and a failure load of 2kN.

Statement of the Problem:

To design and build a steel skew cantilever that is required to show no visible deformation at a vertical working load of 1000N and to fail at 2000N. The objective is to design a structure that satisfies the loading conditions, while keeping weight to a minimum and maintaining design simplicity; to reduce drawing and fabrication time, and making the structure more predictable through analysis. The load is at a horizontal distance of 815mm from a rigid vertical plate. The line of action of the load is 407mm to the right of the normal to the wall through the centre of the main plate when viewed from the front of the main plate. The load is applied through a rig with a 13mm diameter bolt. The main plate has 4 pairs of M6 tapped holes to which the structure may be attached.

Designs Considered:

The main design considered apart from the 4 main member triangulated cantilever, was based around a 3 main member design with cross bracing shown in the diagram to the right. The advantage of this structure is a reduction in weight, holes and rivets thus a huge reduction in cost. However, the design that we came up with was too difficult to analyse and predict during in failure, due to the side planes not being vertical. Also, construction would have been quite difficult because all cross braces would have to attach to the main members at an angle, thus additional plates would have be constructed which would have raised the price dramatically.

The other design considered was based on the 4 main member design but flipped upside down. However, this would mean that the compression member would be comparatively long, increasing the need for cross bracing due to potential buckling. Thus the structure would be no better than the one we have selected only it would cost more due to the additional cross bracing.

The box design was considered, however, it is not very suitable for a skew cantilever as construction would be immensely hard.

Design considerations:

The rig to which the structure was to be attached was inspected to see whether the load plate would fit and to get a general feel for the vertical constraints of the jack.

To prevent a bending moment within the structure, lines of actions of forces in members must cross at a point. Hence in the drawings, lines of actions for every joint are shown to meet at a point within the material. For single cross braces, this line of action is 3/4 of the way in from the edge parallel with the edge.

To make members act as though they were in mode B, the struts had to be rivet together. This was done 40mm from the edges of the struts in question and subsequently the remaining length was divided up into 3 sections at which the boundary of each division was riveted. This was performed on all the double angled struts.

Where possible, the struts coming into connecting plates were made to touch the plate with their edge so that they would be transferring their load in a more direct manner.

We attempted to make the base as wide as possible, for stability hence the connecting plates should go up to the edge of the main plate.

Construction Phase:

The base was the first thing to be constructed as it was easier than the upper members, thus by the time it had been built, experience had been gained and could applied to a more complex construction step (the upper members). The upper members were then constructed and both sets were fitted to the base plate. An additional plate was put in between the connecting plate and the main plate for the tension members to prevent the bolts from tearing out.

The partially completed structure was taken to the measurement deck, where the alignment was checked. It was within 5mm in respect to the horizontal plane, thus we could slightly bias connections so that the alignment became closer to about 3mm. It was then noted that the rig that would connect the load to the load plate needed the load plate to have parallel edges, thus a double bend and an extension of 40mm in the load plate was required to allowed the rig to connect to the load plate. See right hand page for diagram. The load plate was then attached and the structure was checked that it aligned to about 3mm. The cross braces were than fabricated and attached. An attempt was made to work efficiently during construction, my laboratory partner and I finished with 6 hours to spare.

Modifications:

To M4 bolts were used to help keep the two sections of the load plate in alignment to achieve ease of rig attachment. These are attached as shown on the diagram to the right.

A small cross brace was also placed between the two tension members at the top to attempt to prevent rotation of the structure. See right for the diagram. Also there was not enough space for the smallest cross brace connecting the compression members, thus it was not included. Some minor changes in the lengths of some of the members was required to improve alignment. Also some edges of struts had to be cut so that they could rest flat against others to transfer load more effectively.

Cost and Mass of Structure:

The mass was 2.52kg, which is heavy in comparison to the other groups, but not the heaviest. The material cost was 120.5 and the labour cost was 282 giving a total of 452.5, once again the cost ranked high amongst the other groups. However, considering the magnitude of the mass, if the cost saving strategies had not been applied then the cost would have been about 30 higher. These cost saving techniques consisted of using a hole to not only mount the members to connecting sheet metal but also a cross brace, thus saving a rivet, a hole and some time during fabrication. Depending on the forces, this technique could be slight disadvantage, the joint would now be in double sheer, and the rivet would be under greater loading. However, this effect would be small due to the small forces in the cross braces.

Test results and Observations:

The structure had a very slight amount of visible deformation at the working load of 1kN, and finally failed at 2.57kN. This was mainly due to the rightmost (looking at the front plate) compression member 5 buckling inwards at a position closer to the wall than the intersection between member 10 and 11. Another noted deformation was that the metal plates (A and B) connecting the main plate to the compression members had been bent inwards towards the main plate as the corners of the A and B were not touching the main plate. This meant that as the compression force in member 10 and 11 grew the force on the corner increased and cause deformation of the connecting plate. If the buckling in the compression member had not occurred, it would be conceivable that this would be the next location for failure.

Suggested Modifications to Improve Performance:

Using another cross brace in a sense parallel to the main plate between the lower main compression members 10 and 11 would have prevented the buckling that caused the main failure from occurring. The geometry of the proposed cross brace would force the member to become stockier thus its critical stress would be much higher, allowing us to once again us mode A with a 9.5mm by 9.5mm of thickness 0.8mm.

If the holes for the bent plates that connects the main compression members 3 and 5 to the main plate were moved such that the corner of the connecting plate lay within the normal of the edge of the main plate, then this would reduce deformation of the connecting plate and hence the structure. If these connecting bent plates were to be the first point of failure, the modifications described would increase the failure load by postponing the tearing of the connecting plates.

Conclusions:

The main failure as discussed was mode B buckling of the longest compression member due to insufficient cross bracing. It would be interesting to rebuild the cantilever with the improvements and even have an entire redesign. One can learn many things from analyzing a failure. For example how to improve the structure and more importantly how to go about design in the first place.