The beam shown is fabricated of a nickel alloy for which the endurance limit in bending is 289 MPa, the yield strength is 300 MPa, and the ultimate strength is 570 MPa. The thickness of the beam is uniform and equal to 50 mm. The stress concentration factor đue to the fillet at B is 1.3. The applied load ranges from a downward load P to an upward load ½ P as shown. Use factors of safety of 4 with respect to fatigue, 3 with respect to the ultimate strength, and 2 with respect to yielding and determine the maximum permissible load P using (a) the Gerber Parabola, (b) the Goodman Straight Line, and (c) the Soderberg Straight Line. P 200 mm 160 mm -0.5 m -0.5 m- 1.0m (b) The Goodman Straight Line containing a factor of safety is given by Eq. 380P 1140P =D1 o, FS o,FS +. =D1 570x10/3 289x10°/4 The solution of the above equation leads to P= 56.2 kN (c) The Soderberg Straight Line with a factor of safety is expressed by Eq. (11.7): 380P 1140P =1 =1 o, FS 0,FS 300x10/2 289x10*/4 Solving this linear equation yields P=54.6 kN (b) The Goodman Straight Line containing a factor of safety is given by Eq. =D1 380P 1140P =1 o,FS 0,FS 570x10/3 289x10/4 The solution of the above equation leads to P= 56.2 kN (c) The Soderberg Straight Line with a factor of safety is expressed by Eq. (11.7):
The beam shown is fabricated of a nickel alloy for which the endurance limit in bending is 289 MPa, the yield strength is 300 MPa, and the ultimate strength is 570 MPa. The thickness of the beam is uniform and equal to 50 mm. The stress concentration factor đue to the fillet at B is 1.3. The applied load ranges from a downward load P to an upward load ½ P as shown. Use factors of safety of 4 with respect to fatigue, 3 with respect to the ultimate strength, and 2 with respect to yielding and determine the maximum permissible load P using (a) the Gerber Parabola, (b) the Goodman Straight Line, and (c) the Soderberg Straight Line. P 200 mm 160 mm -0.5 m -0.5 m- 1.0m (b) The Goodman Straight Line containing a factor of safety is given by Eq. 380P 1140P =D1 o, FS o,FS +. =D1 570x10/3 289x10°/4 The solution of the above equation leads to P= 56.2 kN (c) The Soderberg Straight Line with a factor of safety is expressed by Eq. (11.7): 380P 1140P =1 =1 o, FS 0,FS 300x10/2 289x10*/4 Solving this linear equation yields P=54.6 kN (b) The Goodman Straight Line containing a factor of safety is given by Eq. =D1 380P 1140P =1 o,FS 0,FS 570x10/3 289x10/4 The solution of the above equation leads to P= 56.2 kN (c) The Soderberg Straight Line with a factor of safety is expressed by Eq. (11.7):
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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Transcribed Image Text:The beam shown is fabricated of a nickel alloy for which the endurance limit in bending is 289 MPa,
the yield strength is 300 MPa, and the ultimate strength is 570 MPa. The thickness of the beam is
uniform and equal to 50 mm. The stress concentration factor due to the fillet at B is 1.3. The applied
load ranges from a downward load P to an upward load P as shown. Use factors of safety of 4 with
respect to fatigue, 3 with respect to the ultimate strength, and 2 with respect to yielding and determine
the maximum permissible load P using (a) the Gerber Parabola, (b) the Goodman Straight Line, and
(c) the Soderberg Straight Line.
P
200 mm
160 mm
-0.5 m
0.5 m-
1.0 m
(b) The Goodman Straight Line containing a factor of safety is given by Eq.
380P
1140P
+
=1
o,FS o,FS
570x10/3 289x10/4
The solution of the above equation leads to
P= 56.2 kN
(c) The Soderberg Straight Line with a factor of safety is expressed by Eq. (11.7):
380P
300x10/2 289x10/4
o,
3D1
1140P
o, FS 0, FS
Solving this linear equation yields
P= 54.6 kN
(b) The Goodman Straight Line containing a factor of safety is given by Eq.
380P
1140P
-=1
o FS o, FS
570x10/3 289x10/4
The solution of the above equation leads to
P= 56.2 kN
(c) The Soderberg Straight Line with a factor of safety is expressed by Eq. (11.7):
σ.
380P
1140P
o FS 0, FS
300x10/2 289x10/4
Solving this linear equation yields
P= 54.6 kN
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