The two rods (A-B and B-C) shown in the left panel are connected by pins at A, B, and C. The cross sections of A-B and B-C are 10mm×13mm and 10mm×10mm, respectively. The bilinear stress-strain relation shown in the right panel is for the material used to make the two rods, where Ei is the slope of the stress-strain curve for stresses between 0 and 80 MPa and E2 is the slope for stresses larger than 80 MPa. Note that Hooke's law is only valid for stresses up to 80 MPa.
Design Against Fluctuating Loads
Machine elements are subjected to varieties of loads, some components are subjected to static loads, while some machine components are subjected to fluctuating loads, whose load magnitude tends to fluctuate. The components of a machine, when rotating at a high speed, are subjected to a high degree of load, which fluctuates from a high value to a low value. For the machine elements under the action of static loads, static failure theories are applied to know the safe and hazardous working conditions and regions. However, most of the machine elements are subjected to variable or fluctuating stresses, due to the nature of load that fluctuates from high magnitude to low magnitude. Also, the nature of the loads is repetitive. For instance, shafts, bearings, cams and followers, and so on.
Design Against Fluctuating Load
Stress is defined as force per unit area. When there is localization of huge stresses in mechanical components, due to irregularities present in components and sudden changes in cross-section is known as stress concentration. For example, groves, keyways, screw threads, oil holes, splines etc. are irregularities.
![The two rods (A-B and B-C) shown in the left panel are connected by pins at A, B, and C. The
cross sections of A-B and B-C are 10mm×13mm and 10mm×10mm, respectively. The bilinear
stress-strain relation shown in the right panel is for the material used to make the two rods, where
Ei is the slope of the stress-strain curve for stresses between 0 and 80 MPa and E2 is the slope for
stresses larger than 80 MPa. Note that Hooke's law is only valid for stresses up to 80 MPa.
A
1
1
B
0.900 m
3
P = 30 kN
2.44 m
C
σ MPa
80
E₂ = 40 GPa
E₁ = 80 GPa
E
a) Given the conditions above, find the axial elongation for each rod when subjected to
P=30KN.
b) Find the final position of Point B due to the applied load P at that location. Hint: Assume
point B moves by unknown amounts Ax and Ay from its initial position, and then use right
triangles to write the known final lengths of the cables in terms of Ax and Ay. The equations
can be simplified by assuming terms Ax² and Ay² are so small they can be neglected.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0b19c45c-45ce-4c27-bac7-d4347db4e836%2F9bfcbfba-f9dd-4a41-a5f7-1a3e8e2d46d6%2Fd303uh_processed.png&w=3840&q=75)
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