1. A rectangular plate 50 mm x 10 mm with a hole 10 mm diameter is subjected to an axial load of 10 kN. Taking stress concentration into account, find the maximum stress induced. [Ans. 50 MPa]
1. A rectangular plate 50 mm x 10 mm with a hole 10 mm diameter is subjected to an axial load of 10 kN. Taking stress concentration into account, find the maximum stress induced. [Ans. 50 MPa]
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Related questions
Question
100%
exercise number 1,2,3,5,8,13
![factor (q) may be obtained. For r = 4 mm, we have q = 0.93.
.. Fatigue stress concentration factor,
K, = 1 + q (K, – 1) = 1 + 0.93 (1.62 – 1) = 1.58
Using this value of K,instead of K, a new value of d may be calculated. We see that magnitudes of K,and
K, are very close, therefore recalculation will not give any improvement in the results already obtained.
EXERCISES
1. A rectangular plate 50 mm × 10 mm with a hole 10 mm diameter is subjected to an axial load of 10 kN.
Taking stress concentration into account, find the maximum stress induced.
[Ans. 50 MPa]
2. A stepped shaft has maximum diameter 45 mm and minimum diameter 30 mm. The fillet radius is 6
mm. If the shaft is subjected to an axial load of 10 kN, find the maximum stress induced, taking stress
[Ans. 22 MPa]
concentration into account.
3. A leaf spring in an automobile is subjected to cyclic stresses. The average stress = 150 MPa; variable
stress = 500 MPa; ultimate stress = 630 MPa; yield point stress = 350 MPa and endurance limit = 150
MPa. Estimate, under what factor of safety the spring is working, by Goodman and Soderberg formulae.
[Ans. 1.75, 1.3]
4. Determine the design stress for bolts in a cylinder cover where the load is fluctuating due to gas
pressure. The maximum load on the bolt is 50 kN and the minimum is 30 kN. The load is unpredict-
able and factor of safety is 3. The surface of the bolt is hot rolled and the surface finish factor is 0.9.
During a simple tension test and rotating beam test on ductile materials (40 C 8 steel annealed), the
following results were obtained :
Diameter of specimen = 12.5 mm; Yield strength = 240 MPa; Ultimate strength = 450 MPa; Endurance
limit = 180 MPa.
[Ans. 65.4 MPa]
5. Determine the diameter of a tensile member of a circular cross-section. The following data is given
Maximum tensile load = 10 kN; Maximum compressive load = 5 kN; Ultimate tensile strength = 600
MPa; Yield point = 380 MPa; Endurance limit = 290 MPa; Factor of safety = 4; Stress concentration
factor = 2.2
[Ans. 24 mm]
6. Determine the size of a piston rod subjected to a total load of having cyclic fluctuations from 15 kN in
compression to 25 kN in tension. The endurance limit is 360 MPa and yield strength is 400 MPa. Take
impact factor =1.25, factor of safety = 1.5, surface finish factor = 0.88 and stress concen
= 2,25.
[!
234 / 1251
7. A steel connecting rod is subjected to a completely reversed axial load of 160 kN. Sugg
diameter of the rod using a factor of safety 2. The ultimate tensile strength of the ma
MPa, and yield strength 930 MPa. Neglect column action and the effect of stress concentration.
[Ans. 30.4 mm]
8. Find the diameter of a shaft made of 37 Mn 2 steel having the ultimate tensile strength as 600 MPa and
yield stress as 440 MPa. The shaft is subjected to completely reversed axial load of 200 kN. Neglect
stress concentration factor and assume surface finish factor as 0.8. The factor of safety may be taken
as 1.5.
[Ans. 51.7 mm]
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Variable Stresses in Machine Parts
1 221
9. Find the diameter of a shaft to transmit twisting moments varying from 800 N-m to 1600 N-m. The
ultimate tensile strength for the material is 600 MPa and yield stress is 450 MPa. Assume the stress
concentration factor = 1.2, surface finish factor = 0.8 and size factor = 0.85.
[Ans. 27.7 mm]
10. A simply supported shaft between bearings carries a steady load of 10 kN at the centre. The length of
shaft between bearings is 450 mm. Neglecting the effect of stress concentration, find the minimum
diameter of shaft. Given that
Endurance limit = 600 MPa; surface finish factor = 0.87; size factor = 0.85; and factor of safety = 1.6.
[Ans. 35 mm]
1.
Determine the diameter of a circular rod made of ductile material with a fatigue strength (complete
stress reversal) o, = 280 MPa and a tensile yield strength of 350 MPa. The member is subjected to a
varying axial load from 700 kN to – 300 kN. Assume K, = 1.8 and F.S. = 2.
[Ans. 80 mm]
12. A cold drawn steel rod of circular cross-section is subjected to a variable bending moment of 565 N-
m to 1130 N-m as the axial load varies from 4500 N to 13 500 N. The maximum bending moment
occurs at the same instant that the axial load is maximum. Determine the required diameter of the rod
for a factor of safety 2. Neglect any stress concentration and column effect. Assume the following
values:
Ultimate strength
= 550 MPa
Yield strength
= 470 MPa
Size factor
0.85
Surface finish factor
= 0.89
Correction factors
= 1.0 for bending
0.7 for axial load
The endurance limit in reversed bending may be taken as one-half the ultimate strength. [Ans. 41 mm]
13. A steel cantilever beam, as shown in Fig. 6.21, is subjected to a transverse load at its end that varies
from 45 N up to 135 N down as the axial load varies from 110N (compression) to 450 N (tension).
Determine the required diameter at the change of section for infinite life using a factor of safety of 2.
The strength properties are as follows:
Ultimate strength
= 550 MPa
Yield strength
= 470 MPa
Endurance limit
= 275 MPa
45 N
125 mm
110 N 450 N
2d
0.2d
180 mm
135 N
Fig. 6.21
The stress concentration factors for bending and axial loads are 1.44 and 1.63 respectively, at the
[Ans. 12.5 mm]
change of cross-section. Take size factor = 0.85 and surface finish factor = 0.9.
14. A steel shaft is subjected to completely reversed bending moment of 800 N-m and a cyclic twisting
moment of 500N-m which varies over a range of±40%. Determine the diameter of shaft if a reduction
factor of 1.2 is applied to the variable component of bending stress and shearing stress. Assume
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Transcribed Image Text:factor (q) may be obtained. For r = 4 mm, we have q = 0.93.
.. Fatigue stress concentration factor,
K, = 1 + q (K, – 1) = 1 + 0.93 (1.62 – 1) = 1.58
Using this value of K,instead of K, a new value of d may be calculated. We see that magnitudes of K,and
K, are very close, therefore recalculation will not give any improvement in the results already obtained.
EXERCISES
1. A rectangular plate 50 mm × 10 mm with a hole 10 mm diameter is subjected to an axial load of 10 kN.
Taking stress concentration into account, find the maximum stress induced.
[Ans. 50 MPa]
2. A stepped shaft has maximum diameter 45 mm and minimum diameter 30 mm. The fillet radius is 6
mm. If the shaft is subjected to an axial load of 10 kN, find the maximum stress induced, taking stress
[Ans. 22 MPa]
concentration into account.
3. A leaf spring in an automobile is subjected to cyclic stresses. The average stress = 150 MPa; variable
stress = 500 MPa; ultimate stress = 630 MPa; yield point stress = 350 MPa and endurance limit = 150
MPa. Estimate, under what factor of safety the spring is working, by Goodman and Soderberg formulae.
[Ans. 1.75, 1.3]
4. Determine the design stress for bolts in a cylinder cover where the load is fluctuating due to gas
pressure. The maximum load on the bolt is 50 kN and the minimum is 30 kN. The load is unpredict-
able and factor of safety is 3. The surface of the bolt is hot rolled and the surface finish factor is 0.9.
During a simple tension test and rotating beam test on ductile materials (40 C 8 steel annealed), the
following results were obtained :
Diameter of specimen = 12.5 mm; Yield strength = 240 MPa; Ultimate strength = 450 MPa; Endurance
limit = 180 MPa.
[Ans. 65.4 MPa]
5. Determine the diameter of a tensile member of a circular cross-section. The following data is given
Maximum tensile load = 10 kN; Maximum compressive load = 5 kN; Ultimate tensile strength = 600
MPa; Yield point = 380 MPa; Endurance limit = 290 MPa; Factor of safety = 4; Stress concentration
factor = 2.2
[Ans. 24 mm]
6. Determine the size of a piston rod subjected to a total load of having cyclic fluctuations from 15 kN in
compression to 25 kN in tension. The endurance limit is 360 MPa and yield strength is 400 MPa. Take
impact factor =1.25, factor of safety = 1.5, surface finish factor = 0.88 and stress concen
= 2,25.
[!
234 / 1251
7. A steel connecting rod is subjected to a completely reversed axial load of 160 kN. Sugg
diameter of the rod using a factor of safety 2. The ultimate tensile strength of the ma
MPa, and yield strength 930 MPa. Neglect column action and the effect of stress concentration.
[Ans. 30.4 mm]
8. Find the diameter of a shaft made of 37 Mn 2 steel having the ultimate tensile strength as 600 MPa and
yield stress as 440 MPa. The shaft is subjected to completely reversed axial load of 200 kN. Neglect
stress concentration factor and assume surface finish factor as 0.8. The factor of safety may be taken
as 1.5.
[Ans. 51.7 mm]
Тop
Contents
Variable Stresses in Machine Parts
1 221
9. Find the diameter of a shaft to transmit twisting moments varying from 800 N-m to 1600 N-m. The
ultimate tensile strength for the material is 600 MPa and yield stress is 450 MPa. Assume the stress
concentration factor = 1.2, surface finish factor = 0.8 and size factor = 0.85.
[Ans. 27.7 mm]
10. A simply supported shaft between bearings carries a steady load of 10 kN at the centre. The length of
shaft between bearings is 450 mm. Neglecting the effect of stress concentration, find the minimum
diameter of shaft. Given that
Endurance limit = 600 MPa; surface finish factor = 0.87; size factor = 0.85; and factor of safety = 1.6.
[Ans. 35 mm]
1.
Determine the diameter of a circular rod made of ductile material with a fatigue strength (complete
stress reversal) o, = 280 MPa and a tensile yield strength of 350 MPa. The member is subjected to a
varying axial load from 700 kN to – 300 kN. Assume K, = 1.8 and F.S. = 2.
[Ans. 80 mm]
12. A cold drawn steel rod of circular cross-section is subjected to a variable bending moment of 565 N-
m to 1130 N-m as the axial load varies from 4500 N to 13 500 N. The maximum bending moment
occurs at the same instant that the axial load is maximum. Determine the required diameter of the rod
for a factor of safety 2. Neglect any stress concentration and column effect. Assume the following
values:
Ultimate strength
= 550 MPa
Yield strength
= 470 MPa
Size factor
0.85
Surface finish factor
= 0.89
Correction factors
= 1.0 for bending
0.7 for axial load
The endurance limit in reversed bending may be taken as one-half the ultimate strength. [Ans. 41 mm]
13. A steel cantilever beam, as shown in Fig. 6.21, is subjected to a transverse load at its end that varies
from 45 N up to 135 N down as the axial load varies from 110N (compression) to 450 N (tension).
Determine the required diameter at the change of section for infinite life using a factor of safety of 2.
The strength properties are as follows:
Ultimate strength
= 550 MPa
Yield strength
= 470 MPa
Endurance limit
= 275 MPa
45 N
125 mm
110 N 450 N
2d
0.2d
180 mm
135 N
Fig. 6.21
The stress concentration factors for bending and axial loads are 1.44 and 1.63 respectively, at the
[Ans. 12.5 mm]
change of cross-section. Take size factor = 0.85 and surface finish factor = 0.9.
14. A steel shaft is subjected to completely reversed bending moment of 800 N-m and a cyclic twisting
moment of 500N-m which varies over a range of±40%. Determine the diameter of shaft if a reduction
factor of 1.2 is applied to the variable component of bending stress and shearing stress. Assume
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Contents
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