Introduction:
EXECUTIVE SUMMARY:
Many famous scientists have left us with much to appreciate and be thankful to their work. If someone thinks of how much clearer the mysteries of the world are to us now just on the basis of what they left us behind. Its remarkable how technology and science is taking one step ahead each and every single ongoing day. “Standing on the shoulder of giants”.
The assignment below has been divided into 3 major parts.
1: Iso-Static and Hyper Static.
Iso- static also called as determinate system are the ones that can enable us to calculate all the unknown forces given.
Hyper-static also called as in-determinate systems are the ones that do not enable us to calculate all the unknowns by the three equations of equilibrium.
2: Hooke’s Law, Poisson’s Ratio and Modulus of rigidity.
Hooke’s law, Poisson’s ratio and shear modulus (modulus of rigidity) all share a common bond. They are considered to be individually the same for a specific material. hooke’s law is formulated as F=kx; Poisson’s ratio is formulated as = (lateral strain / axial strain) and shear modulus is formulated as G= E/(2(1+" " )).
3: polar moment of inertia and angle of twist.
Determinate systems: (ISO-STATIC)
A system is considered statically determinate if the support reaction or unknown forces can be calculated by all three the forces of equilibrium equations. The equations can be solved independently. The equations are as follow:
∑x forces = 0
∑y forces= 0
∑ moments about a point= 0
Some of the examples of iso-static are: cantilever beams, supported beams, arches.
In-determinate systems: (HYPER-STATIC):
A system is considered as statically in-determinate system if unknown forces exceed the number of e...
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... proportional to shear modulus and polar moment of inertia.
Below is an example of angle of twist:
Rate of Twist:
Rate of twist is formulated as:
dφ/dx = T/(G(Ip))
It is directly proportional to the torque and inversely proportional to torsional rigidity (G*Ip).
Referencing:
Mechanics of Material 8th edition (R.C. Hibbeler)
Mechanics of Material pg:52 (James Gere & Barry Goodno)
Plastics Engineering manufacturing and handbook (Volume 2) (Dominik V Rosato, Donald V Rosato, Nick R Schott) PAGE: 1300-1303
Engineering Physics 2nd edition (K Rajagopal) PAGE: 7-12
Mechanics of Material 3rd edition (Roy R Craig Jr)
Mechanics of Material 2nd SI edition (Andrew Pytoll & Jaan Musalaas) PAGE: 342
Mechanics of Material 8th edition (James M.Gere & Barry J.Goodno)
Structural and Stress Analysis Arnold publishers (T.H.G. Megson) PAGE: 158
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