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Mechanics of materials twist
Torsion and deformation, shearing, including the concept of torsion, External couple moment and torque, Pure shear, torsional deformation of circular axis and stiffness conditions, etc.
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Mechanics of materials twist
- bacteria
This is a mind map about bacteria, and its main contents include: overview, morphology, types, structure, reproduction, distribution, application, and expansion. The summary is comprehensive and meticulous, suitable as review materials.
- Plant asexual reproduction
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- Reproductive development of animals
This is a mind map about the reproductive development of animals, and its main contents include: insects, frogs, birds, sexual reproduction, and asexual reproduction. The summary is comprehensive and meticulous, suitable as review materials.
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- Outline
twist
twist concept
Force characteristics: The rod is acted upon by a pair of equal and opposite external force couples whose action surfaces are perpendicular to the axis.
Deformation characteristics: Each cross section between the action surfaces of the two force couples rotates relative to each other around the axis.
External couple moment and torque
Calculation of external torque
Torque calculation
The concept of torque: The torsionally deformed rod is often called a torsion axis, and the internal force on the cross section of the torsion axis is called torque (MT)
Find torque using cross-section method
The rules for positive and negative torque: Determined by the right-hand screw rule, if the torque vector is consistent with the normal line outside the section, the torque is positive; otherwise, it is negative.
Torque diagram
pure shear
Torsional stress experiment on thin-walled circular tubes
Experimental observations
Each circle rotates relative to the axis, and the shape, size, and distance remain unchanged. Each longitudinal line is inclined at the same angle and remains a straight line, and the surface rectangle becomes a parallelogram.
There is no axial or transverse normal strain in the micro-element body. There is shear strain perpendicular to the radial direction, and all shear deformations on the circumference are the same.
Each point on the circumference has no normal stress in the axial and transverse directions, and has the same shear stress in the direction perpendicular to the radius.
Assumption: Since the wall is very thin, it can be assumed that the shear stress is uniformly distributed along the wall thickness
in conclusion
1) There is no normal stress at any point on the cross section of the thin-walled circular tube. 2) The cross-section of a thin-walled circular tube has the same shear stress in the direction perpendicular to the radius.
theorem
pure shear
Shear Stress Twin Equivalence Theorem
Shear Hooke's Law
Circular shaft torsional deformation and stiffness condition
Round shaft torsional deformation
Circular shaft torsional stiffness conditions
condition
Stiffness check
Section size design
Maximum external load calculation
On the torsion cross section of the circular axis stress and strength conditions
experiment
Observe phenomena
plane hypothesis
Qualitative conclusion
Three-way relation method for calculating stress on cross section
deformation relationship
physical relationship
static relationship
General formula for torsional shear stress
Conditions of Use
maximum torsional shear stress
Torsional section coefficient
polar moment of inertia
Strength conditions for circular shaft torsion
Strength condition
Strength condition application
Strength Check
Section size
Find the maximum external load