- #1
Seraph042
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Homework Statement
Shaft AB is fixed at point A and is subjected to a torque T
= 2.5 kN·m applied at point B and an axial force P = 30 kN applied at
point C.
The actual shaft specifications (type of material, prismatic / changing cross sections are left up to us and is NOT the point of my question)
Homework Equations
[tex]\delta[/tex] = PL/AE
P = force, L = length, A = cross-sectional area, E = elastic modulus
[tex]\phi[/tex] = TL/GIp
T = torque, L = length, G = shear modulus, Ip = polar moment of inertia
The Attempt at a Solution
I am basically treating this as 1 deformation problem and 1 torsion problem
For the deformation / axial part:
After cutting the sections, I find that RA = P and RB = P also
And thus,
[tex]\delta[/tex]total = [tex]\delta[/tex]1 + [tex]\delta[/tex]2
Where
[tex]\delta[/tex]1 = PLAB/AABEAB
And
[tex]\delta[/tex]2 = PLBC/ABCEBC
For the torsion part:
Here is where I am very unsure of what to do. I know there will be a reaction torque at A, but will point C have one also?
Right now I've got this -
To + TC + TA = 0
=> To = TA - TC
And
[tex]\phi[/tex]1 = [tex]\phi[/tex]2
Such that
[tex]\phi[/tex]1 = TABLAB/GABIP,AB
And
[tex]\phi[/tex]1 = (TAB-To)LBC/GBCIP,BC
Am I on the right track? Where is my analysis flawed ?