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A round AB bar (L = 600 mm in length and with Ø = 55 mm of diameter) is machined from the heat-treated AISI 1060 steel (quenched and tempered at T = 1200 °C) will be analysed as a candidate for static structural application in the aerospace sector. A system of external loadings acting on the bar is depicted as in Fig. 1 where the two vertical bars OA and BC (L= 280 mm each) forming a working mechanism comprising OABC and can be assumed to be of a one-piece structure. As such, the effect of stress concentration factors due to geometrical discontinuities can be discounted. A summary of the three loadings are given as follows;

A round AB bar (L = 600 mm in length and with Ø = 55 mm of diameter) is machined from the heat-treated AISI 1060 steel (quenched and tempered at T = 1200 °C) will be analysed as a candidate for static structural application in the aerospace sector. A system of external loadings acting on the bar is depicted as in Fig. 1 where the two vertical bars OA and BC (L= 280 mm each) forming a working mechanism comprising OABC and can be assumed to be of a one-piece structure. As such, the effect of stress concentration factors due to geometrical discontinuities can be discounted. A summary of the three loadings are given as follows;

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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A round AB bar (L = 600 mm in length and with Ø = 55 mm of diameter) is machined from the heat-treated AISI 1060 steel (quenched and tempered at T = 1200 °C) will be analysed as a candidate for static structural application in the aerospace sector. A system of external loadings acting on the bar is depicted as in Fig. 1 where the two vertical bars OA and BC (L= 280 mm each) forming a working mechanism comprising OABC and can be assumed to be of a one-piece structure. As such, the effect of stress concentration factors due to geometrical discontinuities can be discounted. A summary of the three loadings are given as follows; 1. Axial force with a magnitude F = 28 kN (along the x-axis) 2. Torsional load with a magnitude T = 2,250 N•m (in yz-plane) 3. Bending moment with a magnitude of M = 1,100 N•m (in xy-plane) In your design exercise for the bar by evaluating the state of plane stress; a) Sketch a clear 2D free-body diagram (FBD) for the AB bar (in xz-plane) in response to all the acting loads. Subsequently, plot a shear stress (V) and bending moment diagram (M) of the bar and determine a location on the structure as the most critical point and justify your selection. b) For the stress system from such critical element in (a), plot a Mohr's circle to determine the corresponding max. and min. normal stress (principal stresses) as well as the max. shearing magnitude. Determine the orientation where these out-of--plane principal stress occurs, c) Compare the safety factor, n, of the bar when it's designed according to Tresca's max. shearing stress (MSS) and von-Mises' distortion energy (DE) theories, d) From the magnitude of n from the MSS method in (c) above, devise a diameter of the new bar if its resulting safety margin from those computed by the DE criterion is to be kept identical, assuming that it is machined from the same material, and e) Eventually, determine the weight ratio improvement of the bar after such a revised diameter is proposed.
Transcribed Image Text:A round AB bar (L = 600 mm in length and with Ø = 55 mm of diameter) is machined from the heat-treated AISI 1060 steel (quenched and tempered at T = 1200 °C) will be analysed as a candidate for static structural application in the aerospace sector. A system of external loadings acting on the bar is depicted as in Fig. 1 where the two vertical bars OA and BC (L= 280 mm each) forming a working mechanism comprising OABC and can be assumed to be of a one-piece structure. As such, the effect of stress concentration factors due to geometrical discontinuities can be discounted. A summary of the three loadings are given as follows; 1. Axial force with a magnitude F = 28 kN (along the x-axis) 2. Torsional load with a magnitude T = 2,250 N•m (in yz-plane) 3. Bending moment with a magnitude of M = 1,100 N•m (in xy-plane) In your design exercise for the bar by evaluating the state of plane stress; a) Sketch a clear 2D free-body diagram (FBD) for the AB bar (in xz-plane) in response to all the acting loads. Subsequently, plot a shear stress (V) and bending moment diagram (M) of the bar and determine a location on the structure as the most critical point and justify your selection. b) For the stress system from such critical element in (a), plot a Mohr's circle to determine the corresponding max. and min. normal stress (principal stresses) as well as the max. shearing magnitude. Determine the orientation where these out-of--plane principal stress occurs, c) Compare the safety factor, n, of the bar when it's designed according to Tresca's max. shearing stress (MSS) and von-Mises' distortion energy (DE) theories, d) From the magnitude of n from the MSS method in (c) above, devise a diameter of the new bar if its resulting safety margin from those computed by the DE criterion is to be kept identical, assuming that it is machined from the same material, and e) Eventually, determine the weight ratio improvement of the bar after such a revised diameter is proposed.
T = 2,250 N m F = 28 kN Ø = 55 mm M, = 1,100 N-m 280 mm Fig. 1. System of stress acting on OABC structural component ww 009
Transcribed Image Text:T = 2,250 N m F = 28 kN Ø = 55 mm M, = 1,100 N-m 280 mm Fig. 1. System of stress acting on OABC structural component ww 009
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