This problem is based on problem 4-109 from the textbook. The figure shows a sch

Question

This problem is based on problem 4-109 from the textbook. The figure shows a schematic drawing of a mechanical system, in this case a vehicular jack that is to be designed to support a maximum mass of 300 kg with a design (or safety) factor of 3.50. The opposite-handed threads on the two ends of the screw are cut to allow the link angle theta to vary from 15 to 70 degree. The links are to be machined from AISI 1010 hot-rolled steel bars (E = 207GPa). Each of the four links is to consist of two bars, one on each side of the central bearings. The bars are to be 350 mm long and have a bar width w of 30 mm. This structure can be analyzed as a truss. Using this analysis, what link(s) will support the largest force? What is this force in terms of the Weight (W)? For the link(s) that support the largest force: Apply the safety factor to find the design force you need to consider in dimensioning the bars. Then, using the Euler formula, find the minimum depth required to support the design force for out-of-plane buckling. Use recommended values for the end-condition constant. Using this minimum depth, find the slenderness ratio and compare it to the critical slenderness ratio, computed with a yield strength of 180 MPa. Are we justified to use the Euler formula? Would the depth you found in 2 be safe? Although it is not as critical, find the slenderness ratio for in-plane buckling. The bearings impose a both-ends-rounded/pivoted end condition. What buckling formula should we use for this analysis? Based on the slenderness ratio from point 4, and the dimensions found in 2, find the critical load the bar will support before in-plane buckling occurs. What is the safety factor for in-plane buckling? Due to manufacturing tolerances, the bearings could potentially be mounted with a 0.01 mm out-of- plane offset from the neutral axis of the bars. Use the secant formula and the dimensions you have already determined to find the critical load for out-of-plane buckling. Write in your homework the secant formula and replace the known values. Then use Matlab or your calculator solver to solve for the load and report it. What would be our safety factor now?

Explanation / Answer

As this ia four link mechanism

under the analysis of trusses the bottom links support the maximum load.

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