Mechanics Of Deformable Bodies Flashcards
A force perpendicular to the section is…
Axial
A force parallel to the section is…
Shear
Moment parallel to the cross section…
Bending
Moment perpendicular to the cross section…
Torsion
External forces cause…
Change in the state of motion of a body
An external force is…
A force that develops at the surfaces of contact between bodies
Internal forces cause…
Deformation
What is failure (the engineering kind of failure)?
When an object no longer functions as intended
Failure is dependent on what 2 things?
Applied force and cross sectional area
What is the formula for stress?
Stress = force / area
Definition of stress…
Force acting per unit area.
A material is continuous if…
Uniform distribution of matter; no voids
The material is cohesive if…
All portions are connected together; No breaks, cracks or separations
A homogeneous material has…
Same physical and mechanical properties all throughout
And isotropic material has…
Same properties in all directions
A prismatic object has..
Constant cross-sectional area
Average normal stress is… And it is represented by the Greek letter…
Average normal stress is when the force is acting perpendicular to the cross section. Represented by sigma ( looks like o ).
If the force is parallel to the object the stress is called… And it is represented by the Greek letter…
Average sheer stress… Tau (looks like T)
The unit of stress is called the…
Pascal 1 N/m^2
What are the three design considerations?
Strength, serviceability, economy
What is strength?
The actual load a structure can carry
What is serviceability?
Resistance to vibrations, deformations, deflections, cracks. Overall functionality.
What is economy?
Most efficient and cost-effective design
What Greek letter represents deformation?
Delta (looks like d)
What causes deformation?
When forces are applied or temperature is changed
Define strain.
Normal strain is the change in length. Shear strain is the angular change between two perpendicular segments.
Normal stresses lead to…
Normal strain
Strain is represented by the Greek letter…
Epsilon (looks like a reversed 3)
Normal strain is calculated with the formula…
Strain = deformation/original length (E=d/L)
Is the object gets longer the normal strain is…
Positive
What is shear strain?
Angular change between 2 perpendicular segments. A change in shape.
What is the formula for shear strain?
Gamma= pi/2 - theta
A … is used to measure elongation…
Extensometer
What does a universal testing machine do?
Measures stress and strain
What are the two types of stress strain diagrams and what’s the difference between them?
There’s conventional and true. A conventional diagram uses the original dimensions while a true diagram uses the actual dimensions of the material the moment the load is applied.
What are the four ways steel behaves?
Elastic behavior, Yielding, Strain hardening, necking
What is elastic behavior?
When you remove the load it will returns to its original shape
The upper stress limit is called…
Proportional limit
The elastic limit is…
The point past the proportional limit where the material could still respond elastically
What is yielding?
The specimen will continue to deform without load increase.
Plastic deformation is…
Permanent deformation
Stress that causes yielding is called…
Yield stress or yield point
The maximum stress is called…
Ultimate stress or ultimate strength
What happens during necking (the engineering kind)?
The cross sectional area decreases causing the load carrying capacity of the object to decrease.
The specimen breaks at the…
Fracture stress
Who formalized the concept of stress and strain?
Thomas Young
Young’s modulus or the modulus of elasticity is given by…
Stress / strain ( gives the slope of the elastic region)
The modulus of rigidity or the shear modulus is given by…
G = shear stress /shear strain (g=T/y)
The modulus of resilience is…
The amount of energy a material can take before experiencing permanent deformation. In the graph it is the area where stress is proportional to strain.
The modulus of toughness is…
The amount of energy an object can take before it breaks. It is the entire area of the graph.
Poisson’s ratio is…
Ratio between lateral strain and longitudinal strain. Represented by V
An object is ductile if…
Can undergo large deformations before failing.
An object is brittle if…
It experiences little or no yielding before failing.
What are the types of failure?
Elastic (excessive elastic def.), Slip (excessive plastic def. due to slip), Creep (excessive plastic def. over a long period of time under constant stress), fracture (complete separation)
The engineering equivalent of wiggle room or allowance is called…
The factor of safety or ignorance
What is the formula for factor of safety?
Ultimate stress/working stress
Factor of safety is always …
> 1
What is Torque?
A twisting couple
Angle of twist is proportional to…
Applied torque and length of shaft
In a circle, after torque is applied every plane remains…
Plane and undistorted because a circle is axisymmetric.
What happens when non-axisymmetric shafts are subjected to torsion?
The cross sections become distorted.
Shear strain is proportional to…
Twist and radius
Shear strain is proportional to…
The distance from the center.
Maximum shear strain in circular shafts occurs…
At the outermost points
What is the polar moment of inertia?
Ability of geom to resist twisting
What is the formula for angle of twist?
Phi = TL / JG where T is torque, L is length of shaft, G is the modulus of rigidity, J is the polar moment of inertia
What is the formula for polar moment of inertia?
Pi/2 * r^4
When subjected to torsion a ductile material breaks along
The plane of maximum shear (perpendicular to shaft axis)
When subjected to torsion a brittle material breaks at an angle of…
45 degrees along the shaft axis
What re the principal considerations in designing transmission shafts?
Power and speed
In designing transmission shafts one should choose materials without exceeding…
Maximum angle of twist and maximum torsional shearing stress
How do you calculate torque giving speed and power?
Power = torque x angular velocity
What is a column?
Straight structural members subjected to compressive axial loads
What are the types of columns and the failure that governs them?
Short-crushing, Long-buckling
What is buckling?
When a structure subjected to compression undergoes visibly large displacements transverse to the load.
What is the formula for the critical load for buckling?
P = pi^2EI/KL^2 ; E is Young’s modulus,I is the moment of inertia of the weaker axis; K is the effective length factor; L is the length of the column
