Mechanics; Chapter 2 Flashcards
Structural Components subjected to tension or compression are know as ____ _____ members.
axially loaded
When determining the changes in lengths of axially loaded members, it is convenient to begin with a ______ ______, since the overall stretching or shortening is analogous to the behavior of a bar in tension or compression.
coil spring
The natural length is also called the ____ _____ (3 different names).
unstressed length
relaxed length
free length
When applying a tensile load to a spring, the spring lengthens by an amount _____ and its final length becomes ______ + ______.
δ
L + δ
L= original length)
δ= (Greek Letter Delta)= elongation or uniaxial deflection;
Define Stiffness for a Spring Provide Equation
Defined as the force required to produce a unit elongation in a linear elastic member
k = P/δ
k=stiffness
p= axial force
δ=elongation
Define Flexibility for a Spring Provide Equation
Defined as elongation produced by a load unit value.
f = δ/P
f=flexibility
p=axial force
δ=elongation (Greek Letter Delta)
Stiffness and flexibility of a spring are ______ of each other.
reciprocals
k=1/f
f=1/k
k= Stiffness
f= flexibility
Flexibility of a spring can easily be determined by measuring the _____ produced by a know load.
elongation (δ)
When a prismatic bar of linear elastic material is loaded ONLY at the ends, we can obtain its length from the equation ______.
δ=PL/AE
δ= Elongation (Greek Letter Delta)
P= Axial force
E= Modulus of Elasticity
L= Length
A= Cross Sectional Area
Explain how the equation for Uniaxial Deflection is derived
For a simple homogenous bar with a constant cross section and a constant applied load, the total deflection of the bar can be determined in terms of P, L, A, and E.
Starting with the one dimensional Hooke’s Law, σ = Eε and substituting P/A for stress and δ/L for strain gives, P/A = E (δ/L) This can be rearranged to give, δ=PL/AE
The product AE is knows as the ____ ____ of the bar.
axial rigidity
If a material is _____ _____, the load and elongation will be proportional.
linear elastic
Uniaxial Deflection (Constant Load, Area and Stiffness);
Provide Elongation Equation for series of bars and explain
If there are a series of bars, then the deflection of each section can be determined and then all deflections summed.
This can be written in equation form as δ total=Σ PiLi/AiEi i
Total Deformation= δ = PL1/A1E1 + PL2/A2E2 + PL3/A3E3
The stiffness (k) and flexibility (f) of a _____ ____ are defined in the same way for a spring. Provide equations
prismatic bar
k = AE/L
f = L/AE
k=stiffness
f=flexibility
A cable is considered an _____ _____ member because it is subjected only to tensile forces
axially loaded
Cables are also known as ______ _____.
wire rope
Cross sectional area of a cable is equal to the cross sectional area of the individual wires, called the ______ ______.
effective area
Under the same tensile load, the elongation of a cable is greater then the elongation of a solid bar of the same material & cross sectional area, because the wire cable _____ ____.
tightens up
Explain the Equations of Compatibility
Equations of Compatibility expresses the fact that the change in length of a bar must be compatible with the conditions at the supports.
Changes in temperature produce expansion, or contraction of structural materials, resulting in ______ ______ & ______ ______.
Thermal Stresses
Thermal Strains
For most structural material, thermal strain (εT) is proportional to the _____ ____. Provide equation α is a property of the material called _____ _____ _____ _____.
Temperature Change
Coefficient of Thermal Expansion
α= Coefficient of Thermal Expansion
ΔT= Change in Temperature
C= Coefficient of thermal expansion
Provide the equation for temperature-displacement relation
δT= εT*L = α*(ΔT)*L δ
T= Temperature elongation
L= Original length
α (alpha)= Coefficient of thermal expansion
(ΔT)= change in temperature
εT= Thermal Strain
The temperature displacement equation can be used to calculate changes in lengths of structural members subjected to uniform _____ _____.
Temperature changes
A ____ ____ ____ with uniform temperature changes will produce thermal strains (and the corresponding changes in Length) without producing any corresponding stresses.
statically determinate structure
A _____ _____ _____ may, or may not develop stresses, depending on the character of the structure and the nature of the temperature change.
statically indeterminate structure
A simple way to produce a change in length is to tighten a bolt or turnbuckle. In the case of a bolt, each turn will cause the nut to travel along a bolt a distance equal to the spacing ____ of the threads (Called the _____ of the threads).
ρ
pitch
δ = n*ρ
n= number of revolutions
Provide equation for a double-acting turnbuckle
δ = 2n*ρ
n= number of revolutions
