MEGR 2144 Quiz #1-7
What is the normal strain (%, 4 decimal points) under axial loading if the elongation is 4 mm and total length is 6 m?
% Normal Strain = (elongation / length) * 100
Please check correct response regarding strain and Poisson's Ratio.
- If the axial strain is 0.004 and the lateral strain is -0.001, the Poisson's ratio is 0.25. - If the Poisson's ratio is 0.3 and the lateral strain is 0.001, the axial strain is -0.00333. - The lateral and axial strains normally have opposite sign. - For ordinary material, the Poisson's ratio will have a positive value, range from 0 to 0.5.
For a given cross-sectional area, circular tubes are more efficient than a solid bar to transmit torques because
- They have larger torsional rigidity (GIP); - The torsional stiffness, kT, is larger than a solid bar. - Most materials are located closer to the outer surface, and IP is large;
In equation Y max = r*theta = r*theta / L, match the SI unit of each term.
- maximum shear strain = rad - angle of twist per length = rad/m - total angle of twist = rad - L = length, m
For steel, the coefficient of thermal expansion [alpha (a) = 9.6 x 10^-6 / degrees F ]. Calculate the thermal strain for temperature change 444 degrees F (show 4 decimals).
0.0043 [Eq: alpha * temp change]
A rubber band is 11.9 inch long at rest. It stretches 2.7 inch by hanging a weight at one end. Calculate the strain of the rubber band (3 decimal points).
0.227 [Eq: Strain = length stretched / original length]
Match stresses in pure shear: (See Google Doc 8)
1 = A 2 = C 3 = B 4 = D
Dead loads consist of the weight of various structural members and weights of objects that are permanently attached to a structure. The weight of a bridge light pole is considered as a _____1________ load because it is _____2________ attached to the bridge; whereas the weight of a moving vehicle on the bridge is considered as a ______3________load because it is ______4_______ attached to the bridge.
1- dead 2- permanently 3- live 4-temporarily
Matching the signs of shear stresses acting on the following faces and in the following direction. (See image on Google Doc)
1. Acting on + x face and in + y direction = + Shear Stress 2. Acting on which + face and - x direction = on the +y face and - shear stress 3. Acting on - x face and + y direction = - Shear Stress 4. Acting on which - face and - x direction = on the - y face and + shear stress
According to the allowable stress design, if the allowable stress is 133 MPa and the yield stress of the selected material is 244 MPa, what is the factor of safety used in the design? (two decimals, i.e., 2.34)
1.83 [Eq: SF = Yield Stress / Allowable Stress]
If the maximum shear stress in axially loaded bar is 6 MPa, calculate the maximum normal stress in MPa.
12 [Simplified Eq: Normal Stess = 2*Shear stress] [Actual Eq: Shear Stress = (Normal stress/ 2)*sin 2(45 degrees) ]
Calculate the stress of a tensile force 5976 N on a bar of 4 mm diameter (calculate to 0 decimal point) (MPa).
476 [Eq: Stress = F/A = F/ (pi*r^2) ]
For a prismatic bar of cross-sectional area A, what is the cross-sectional area of the inclined section p-q? (See Google Doc)
A(p-q) = A / cos theta
Please select equations needed to solve statically indeterminate axial structures.
All the above
For a circular bar and a tube, both have the same polar moment of inertia, compare the cross-sectional area Ac, for the circular bar and At for the tube.
At < Ac
If the allowable load for a bridge is 5 tons, what will happen if a 6 ton vehicle drive through the bridge?
Both situations could happen.
What is the compatibility equation that we can use for this statically indeterminate bar. (See Google Docs)
Elongation (AC) + Elongation (BC) = 0
What is the compatibility equation that we can use for this statically indeterminate structure, a steel cylinder encased in a copper tube, both are compressed by a force P.
Elongation (C) = Elongation (S)
For a round bar ABCD with both ends A and D fixed, two constant torque T0 is applied at point B and C as shown. The structure is a statically determinate torsional member.
False
For a statically indeterminate structure, only the thermal strain will be developed.
False
From shear stress in each segment of a round bar with several diameters, T = Tr/Ip, the maximum shear stress in segment i is proportionally increased with the radius of the segment.
False
Hooke's law applies to the nonlinear elasticity.
False
Shear failure along a 45 degree plane of a wood block loaded in compression. The maximum shear stress in an axially loaded bar is only one-half the maximum normal stress. The shear stress may cause failure if the material is as strong in shear as in tension. (See image in Google Doc)
False
Shear stresses act perpendicularly to the surface of the material element.
False
The maximum normal stress under axial loading occurs at theta = +/- 45 degrees .
False
The inclined surface was cut from the corner a. If the length of the cube is l. Match the total force applied in each direction shown in (b). (See Google Doc 7)
Force in +x direction = a Force in -x direction = b Force in +y direction = d Force in -y direction = c
According to definitions in the Mechanics of Materials, match the following terms.
If an object is strong enough, we consider it has sufficient - Strength If an object deforms so much that it cannot perform its intended function, we consider it has insufficient - Stiffness If an object bends at some elevated load so that it can no longer continue to perform its function, we consider it has insufficient - Stability
Force applied on an inclined section when the axial force P was applied. (See Google Docs)
N = P cos theta
What is the SI unit for torque?
N.m
What are the US units of Young's modulus?
PSI, KSI
What are the US units of shear stress?
PSI, KSI
What are the US units of stress?
PSI, KSI
What are the US units of the shear modulus G?
PSI, KSI
What are the SI units of Young's modulus?
Pa, MPa, GPa
What are the SI units of shear stress?
Pa, MPa, GPa
What are the SI units of stress?
Pa, MPa, GPa
What are the SI units of the shear modulus G?
Pa, MPa, GPa
Please match the labels on the Fig. 1-10 with proper terms. (See Google Doc)
Proportional limit - A Yield stress - B Ultimate stress - D strain hardening - C-D linear region - O-A
If we know the shear strain and the shear modulus of elasticity, we can calculate the ___________stress.
Shear
For an axially loaded prismatic bar, we have
Stiffness k = EA / L Flexibility f = L / (EA) Axial Rigidity = EA Elongation under load P = PL/ (EA)
The inclined surface was cut from the corner a. If the length of the cube is l. Match the areas for each surface shown in (b). A1=l2 A2=l2tan(theta) A3=l2/cos(theta) (See Google Docs)
Surface A - A1 Surface B - A2 Surface C - A3
Which design provision was based on probability concepts?
The Load and Resistance Factor Design
For an axially loaded prismatic member,
The SI unit of stiffness k is N/m. The SI unit of flexibility f is m/N. The US units of stiffness k is lb/ in. The US unit of flexibility f is in./ lb
When deriving the equation to calculate the maximum shear strain, ( Y max), of a solid circular bar under pure torsion, we have made the following important assumption:
The angle of twist, Theta, is small.
When deriving the equation for the shear stresses in a circular bar under pure torsion (T max = G*r*theta) (G is the shear modulus of the material, r the radius of the bar and theta the rate of change of the angle of twist), we have used the following assumption
The materials is linearly elastic and the Hooke's law for shear applies.
In the equation (elongation = PL/EA), if the unit of load P is N, the unit of length L is m, the unit of cross-sectional area A is m^2. The unit of change in length is _____. Here we used ________ units.
The unit of change in length is m. Here we used SI units.
The inclined surface was cut from the corner a. If the length of the cube is l. What is the force applied to the surface B. (See Google Docs)
Tl^2 tan(theta)
Match the terms with their equations (G - the shear modulus of elasticity, Ip - the polar moment of inertia, and L - the length of the bar).
Torsional rigidity = GIp Torsional stiffness = GIp / L Torsional flexibility = L / GIp
A structure needs periodic check because material strengths over time may change due to corrosion and other effects.
True
Factors of safety are established by groups of experienced engineers. Typical factors of safety range from 1.5 to 3.
True
For a statically determinate structure, no thermal stress will be developed even the thermal strain exists.
True
For a statically indeterminate torsional structure, we need to do the following steps to calculate maximum shear stress and angle of rotation: - Equation of equilibrium - Equation of compatibility - Torque-displacement equation - Solution of equation
True
From shear stress in each segment of a round bar with several diameters, T = Tr / Ip, the maximum shear stress in segment i is NOT affected by diameters of other segments.
True
From the equation for the angle of twist in a round bar with several diameters, theta = TL/GIp, the angle of twist in the segment is proportionally increased with the length of the segment.
True
Hooke's law applies to the linear elasticity.
True
Shear stresses act tangentially to the surface of the material element.
True
Statically indeterminate bar with uniform temperature increase. The thermal strain and the strain by the reaction RA have the same magnitude and opposite signs. (See Google Doc)
True
When a bar is under tension, the maximum shear stress (T max = Stress(x) / 2 ) occurs at theta = -45 degrees. The minimum shear stress (T max = - Stress(x) / 2 ) occurs at theta = + 45 degrees when the tensile stress (stress x) is applied.
True
When we deal with an axial member under loading and temperature change, the strain caused by the load can be determined from the difference between the total strain measured by a strain gage and the strain caused by the temperature change.
True
In the equation G*theta = T/P = T max / r , match the SI unit of each term. (a) T max, (b) T, (c) theta , (d) G
a - shear stress at the outer surface, Pa. b - shear stress at an internal point, Pa. c - angle of twist per unit length, rad/m. d - shear modulus, Pa.
During the 1998 ice storm (ice rain), many power towers in Quebec, Canada collapsed due to the following reason(s):
e: Effects from b and c
A statically determinate member means that the number of unknown variables is ____ the number of equations based on static equilibrium.
equal to
What is the US unit for torque?
lb.ft
What is the SI unit for the polar moment of inertia Ip.
m^4
A statically indeterminate member means that the number of unknown variables is ____ the number of equations based on static equilibrium.
more than
The shear strain is __________(positive, negative) if the angle between two positive faces is reduced.
positive
In the allowable stress design, we use the following strength to calculate the factor of safety.
sometimes the ultimate strength, sometimes the yield strength
When deriving the equation for change in length of an axially loaded member (elongation = PL/EA) , we have made the following assumption(s):
the member only has linearly elastic deformation so that Hooke's law applies.
