MEGR 2144 Final

5

A beam is loaded by a negative bending moment M. The distance from the neutral axis to the top surface is C1, and the distance from the neutral axis to the bottom surface is C2. If C1=2C2, and the maximum tensile stress is 10 MPa, what is the magnitude of the maximum compressive stress?

0

A beam is loaded by a negative bending moment M. The distance from the neutral axis to the top surface is C1, and the distance from the neutral axis to the bottom surface is C2. If C1=2C2, and the maximum tensile stress is 862 MPa, what is the magnitude of the normal stress at the neutral axis?

6

A beam is under a positive bending moment M. The distance from the neutral axis to the top surface is C1, and the distance from the neutral axis to the bottom surface is C2. If C1=2C2, and the maximum tensile stress=3 MPa, what is the magnitude of the maximum compressive stress?

False

A cantilever beam AB is loaded by all kind of loads. The end A is fixed and end B is free. We don't know exactly what kind of load applied to the beam. Fortunately, we know the bending moment M diagram and EI. The area of M/EI diagram equals to the angle of rotation at support A.

True

A cantilever beam AB was supported at A, and had a negative area of the M/EI diagram due to the negative bending moment M. Based on the second moment-area theorem, the tangent deviation from A to B tB/A is negative. Does it mean the point B is below the tangent at A which is aligned with the x direction.

False

A rectangular beam under transverse loading (bending moment and forces perpendicular to the beam axis) always has its maximum shear stress at the neutral surface.

0.241

A rubber band is 10.8 inch long at rest. It stretches 2.6 inch by hanging a weight at one end. Calculate the strain of the rubber band (3 decimal points).

Symmetry Condition that the slope of the deflection curve at middle point is zero. Continuity Condition of Slope that the slope at L/4 obtained from left (before the reinforcement) is equal to the slope obtained from the right (after the reinforcement). Boundary Condition that deflection at both supports are zero Continuity Condition of deflection that the deflection at L/4 obtained from left (before the reinforement) is equal to the deflection obtained from right (after the reinforcement).

A simple beam AB was reinformed in the middle half (from L/4 to 3L/4) and the moment inertia I was doubled at the middle half. Check all conditions that are needed to solve the equation of the deflecion and angle of rotations.

3

A simple beam was loaded by a concentrate load P right at the middle of the beam. The P caused the beam deflection of 2 mm at the middle of the beam. Later, the beam was further loaded by an evenly distributed load q across the whole beam, which increased the beam deflection at the middle of the beam to 5 mm. What is the amount of deflection caused by the evenly distributed load q at the middle of the beam (in mm)?

equal to

A statically determinate member means that the number of unknown variables is ____ the number of equations based on static equilibrium.

more than

A statically indeterminate member means that the number of unknown variables is ____ the number of equations based on static equilibrium.

false

A steel plate is subjected to plane stress and the out-of-plane principal strain is negative while the in-plane principal strains are positive. The largest shear strain occurs in an in-plane direction.

True

A stress element can have only one pair of principal stresses, which are the maximum and minimum normal stresses.

True

A structure needs periodic check because material strengths over time may change due to corrosion and other effects.

A<B<C<D<E

A(circle) B(Square) C(tall Rectangular) D(taller rectangular) E(I beam) If the above shapes are used to build beams and their cross-sectional areas are the same, which of the following statement is correct for their efficiency.

1.83

According to the allowable stress design, if the allowable stress is 168 MPa and the yield stress of the selected material is 307 MPa, what is the factor of safety used in the design? (two decimals, i.e., 2.34)

True

According to the continuity conditions, the deflection and slope determined for the left-hand part of the beam must be equal to the deflection and slope determined for the right-hand part, respectively.

Boundary condition of a pin support the deflection is zero Boundary condition of a roller support the deflection is zero Boundary condition of a fixed support both the deflection and the slope of the deflection are zero

Add boundary conditions for each beam support.

σx+σy

Based on the Figure, choose the correct answer:σx1+σy1 equals to

829.161

Calculate the stress of a tensile force 5,861 N on a bar of 3 mm diameter (calculate to 0 decimal point) (MPa).

dead permanently live temporarily

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 load because it ------ is attached to the bridge; whereas the weight of a moving vehicle on the bridge is considered as a ------ load because it ------- is attached to the bridge.

M=RA*x

Determine the bending moment M in the free-body diagram.

V=RA

Determine the shear force V in the free-body diagram.

the load, weight density of the selected beam, and the allowable stress.

During design of beams for bending stresses, we recalculate the maximum bending moment and required section modolus from

True

During design of beams for bending stresses, we select a trial beam from Table E-1, and recalculate the maximum bending moment and the required section modulus. If the section modulus of the selected beam is greater than the required section modulus, we have successfully completed the design process.

Effects from : Extra load due to the ice attached to the towers Wind loads

During the 1998 ice storm (ice rain), many power towers in Quebec, Canada collapsed due to the following reason(s):

False

During the design of beams for bending stresses, we determine the maximum bending moment due to load only first. Then we determine required section modulus S. From Table E-1, we select a trial beam with a section modulus slight less than the required section modulus.

True

Factors of safety are established by groups of experienced engineers. Typical factors of safety range from 1.5 to 3.

A or B

For Alloy 2014-T6, S1=0, S2=55, if the effective slenderness ratio KL/r is 0, which equation should we use to calculate the allowable stress.

B

For Alloy 2014-T6, S1=0, S2=55, if the effective slenderness ratio KL/r is 10, which equation should we use to calculate the allowable stress.

B

For Alloy 2014-T6, S1=0, S2=55, if the effective slenderness ratio KL/r is 40, which equation should we use to calculate the allowable stress.

C

For Alloy 2014-T6, S1=0, S2=55, if the effective slenderness ratio KL/r is 60, which equation should we use to calculate the allowable stress.

At<Ac

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.

4/3

For a circular beam (radius r) under pure bending, the maximum shear stress will be ________ times of the average shear stress V/A.

equilateral triangle

For a column of given cross-sectional area, which cross-section shape of the following has the highest critical load based on theoretical consideration?

The torsional stiffness, kT, is larger than a solid bar. They have larger torsional rigidity (GIP); Most materials are located closer to the outer surface, and IP is large;

For a given cross-sectional area, circular tubes are more efficient than a solid bar to transmit torques because

elastic stability

For a long column, the most likely failure mode is caused by exceeding the _______ limit.

True

For a plane strain element, the sum of the normal strains in perpendicular direction is a constant, that is,

1, normal stress at theta a 2, normal stress at theta+pi/2 b 3, shear stress at theta c

For a plane stress element, we can use transformation equations to determine normal and shear stress at an angle . Please match the equations for 1) normal stress at , 2) normal stress at θ + π 2, and 3) shear stress at .

the upper part of the beam (y>0, above the neutral surface) is in compression, sx<0 strains on upper part of the beam (y>0, above the neutral surface) are negative

For a positive curvature

A/cos(theta)

For a prismatic bar of cross-sectional area A, what is the cross-sectional area of the inclined section p-q?

False

For a rectangular beam (height h, width b, h>b) under pure bending, if the beam is rotated and now its height is b and width is h, both the maximum tensile stress and the maximum shear stress will be changed.

true

For a rectangular beam (height h, width b, h>b) under pure bending, if the beam is rotated and now its height is b and width is h, the maximum shear stress will be the same since the cross-sectional area bh is the same.

False

For a rectangular beam (height h, width b, h>b) under pure bending, if the beam is rotated and now its height is b and width is h, the maximum shear stress will be the same since the maximum first moment of area Q is not changed.

1.5

For a rectangular beam (height h, width b, h>b) under pure bending, the maximum shear stress will be ________ times of the average shear stress V/A.

False

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.

strength

For a short column, the most likely failure mode is caused by exceeding the _______ limit.

True

For a statically determinate structure, no thermal stress will be developed even the thermal strain exists.

False

For a statically indeterminate structure, only the thermal strain will be developed.

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

For a thin-walled cylindrical pressure vessel, the circumferential stress is twice of the longitudinal stress.

Stiffness k EA/L Flexibility f L/(EA) Axial Rigidity EA Elongation under load P PL/(EA)

For an axially loaded prismatic bar, we have

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

For an axially loaded prismatic member,

inelastic stability

For an intermediate column, the most likely failure mode is caused by exceeding the _______ limit.

0.0002

For steel, the coefficient of thermal expansion is . Calculate the thermal strain for temperature change 24degrees F (show 4 decimals).

simple beam

For the beam in the following figure, if MA is released as the static redundant, the released beam becomes a

deltaB=0

For the following propped cantilever (statically indeterminate) beam, if Rb is released as redundant, and the beam is solved using the method of superposition, the possible compatibility equation is

deltaB=0

For the following propped cantilever (statically indeterminate) beam, if is released as redundant, and the beam is solved using the method of superposition, the possible compatibility equation is

thetaA=0

For the propped cantilever (statically indeterminate) beam, if Ma is released as redundant, and the beam is solved using the method of superposition, the possible compatibility equation is

thetaA=0

For the propped cantilever (statically indeterminate) beam, if is released as redundant, and the beam is solved using the method of superposition, the possible compatibility equation is

N=Pcos(theta)

Force applied on an inclined section when the axial force P was applied.

True

From shear stress in each segment of a round bar with several diameters, , the maximum shear stress in segment i is NOT affected by diameters of other segments.

False

From shear stress in each segment of a round bar with several diameters, , the maximum shear stress in segment i is proportionally increased with the radius of the segment.

(σ1-σ2 )/2

From the Figure, the maximum shear stress is equal to

σ1 and σ2

From the Figure, the principal stresses are

True

From the equation for the angle of twist in a round bar with several diameters, , 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.

False

Hooke's law applies to the nonlinear elasticity.

300 psi

If (σx+σy )/2 is 500 psi, σ2=200 psi tmax =

800 psi

If (σx+σy )/2 is 500 psi, σ2=200 psi σ1=

the structure is unstable.

If a long and slender structure member is loaded by an axial compressive force which is greater than the critical load of the structure member,

stability

If an object bends at some elevated load so that it can no longer continue to perform its function, we consider it has insufficient

stiffness

If an object deforms so much that it cannot perform its intended function, we consider it has insufficient

strength

If an object is strong enough, we consider it has sufficient

Both situations could happen.

If the allowable load for a bridge is 5 tons, what will happen if a 6 ton vehicle drive through the bridge?

linear function of x

If the distributed load q on a beam is 0, the bending moment M is

constant

If the distributed load q on a beam is 0, the shear force V is

quadratic function of x

If the distributed load q on a beam is a constant, the bending moment M is

linear function of x

If the distributed load q on a beam is a constant, the shear force V is

-90 or 135

If the first principal plane occurs at qp1=45o, qp2=

90

If the first principal plane occurs at qp1=45o, the orientation of the planes of maximum positive or negative shear stress, qs1=

6

If the maximum shear stress in axially loaded bar is 3 MPa, calculate the maximum normal stress in MPa.

True

If we know the maximum bending moment M and the section modulus S, we can calculated the maximum normal stress without knowing the Young's modulus E.

Shear

If we know the shear strain and the shear modulus of elasticity, we can calculate the ___________stress.

Area that circumferential stress acts on 2 b t longitudinal stress 2(3.14) r t Effective area that the force P<sub>1</SUB> acts on 2 r b force P₂ 2(3.14) r r

In a thin-walled circular tank, match the areas on which stresses and forces due to internal pressure acting.

False

In a thin-walled circular tank, the longitudinal stress is equal to the circumferential stress.

True

In equation Pcr=π2EI/(L2), we define the critical load that a column can withstand before buckling.

sometimes the ultimate strength, sometimes the yield strength

In the allowable stress design, we use the following strength to calculate the factor of safety.

a shear stress at an internal point, Pa. b shear stress at the outer surface, Pa. c angle of twist per unit length, rad/m d shear modulus, Pa

In the equation G θ = τ ρ = τ max r, match the SI unit of each term. (a)τ max, (b) τ, (c) θ, (d) G

The unit of change in length is m. Here we used SI units.

In the equation 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 m2. The unit of change in length is _____. Here we used ________ units.

The r in the eccentricity ratio is the radius of gyration of the column. The e in the eccentricity ratio is the distance from the load to the neutral axis of the column. The c in the eccentricity ratio is the distance from the top or bottom surface to the neutral axis of the column.

In the equation for the eccentricity ratio (ec/r2), match the parameters with their corresponding definitions.

True

In the shear formula, , at the top surface, the shear stress is zero.

False

In the shear formula, at the bottom surface, the shear stress is zero because Q is not zero and V equals to zero.

True

In the shear formula, at the bottom surface, the shear stress is zero.

True

In the shear formula,,at the bottom surface, the shear stress is zero because Q is zero.

A Positive bending moment B Negative bending moment C Positive shear force D Negative shear force E Negative q of distributed load

Match sign for bending moment, shear force and intensity of distributed load.

e Stress element of point A d Stress element of point B a Stress element of point C b Stress element of point D c Stress element of point E

Match stress elements for points A, B, C, D and E.

1a 2c 3b 4d

Match stresses in pure shear:

Torsional rigidity GIp Torsional stiffness GIp/L Torsional flexibility L/GIp

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).

Acting on + x face and in + y direction=+ shear stress Acting on which + face and - x direction = + y face - shear stress Acting on - x face and + y direction = - shear stress Acting on which - face and - x direction = - y face +shear stress

Matching the signs of shear stresses acting on the following faces and in the following direction. Fig 1-27

radius of curvature m curvature 1/m cross-sectional area m² longitudinal strain m/m

Matching units with parameters:

True

On the maximum shear stress planes of a general plane stress element, the normal stress is equal to the average of two principal stresses.

If the principal stresses are positive, a normal stress on any inclined element will be positive. The minimum shear stress is always negative. There is alwasy a positive maximum shear stress.

Please check correct answers according to the Mohr's circle.

If the Poisson's ratio is 0.3 and the lateral strain is 0.001, the axial strain is -0.00333 . For ordinary material, the Poisson's ratio will have a positive value, range from 0 to 0.5. If the axial strain is 0.004 and the lateral strain is -0.001, the Poisson's ratio is 0.25. The lateral and axial strains normally have opposite sign

Please check correct response regarding strain and Poisson's Ratio.

The shear foce does not change at the point of application of a couple A concentrate force P acting on a beam will produce a sudden change in the shear forcce. A couple acting on a beam will produce a sudden change in the bending moment. The shear force is zero at the point where the bending moment is maximum.

Please check those correct statements:

Force Vector Stress Tensor Length scalar

Please match terms

Proportional limit=A Yield stress=B Ultimate stress=D strain hardening=C-D linear region=O-A

Please match the labels on the Fig. 1-10 with proper terms.

SF1 BM2 SF2 BM1 SF3 BM4 SF4 BM3

Please match the pairs of the shear force disgram and corresponding bending moment diagram.

Shear Force A Beam Loading 1 Shear Force B Beam Loading 4 Shear Force C Beam Loading 2 Shear Force D Beam Loading 3

Please match the shear force diagram with corresponding beam and loading.

All of the above Geometry of deformations Equilibrium equations Compatibility equations Force-deformation relationships

Please select equations needed to solve statically indeterminate axial structures.

quiz 8

Please select right diagram forms for the shear force and bending moment for the beam in the Figure.

False

Positive curvature means the beam is bent concave downward and the center of the curvature is below the beam

True

Positive curvature means the beam is bent concave upward and the center of the curvature is above the beam

there is no shear force (V=0) there is a constant bending moment (M=constant)

Pure bending means that in the beam

False

Shear failure along a 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.

False

Shear stresses act perpendicularly to the surface of the material element.

True

Shear stresses act tangentially to the surface of the material element.

True

Shear stresses are zero on the principal planes.

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. True

true

Strains can be measured using a simple component called a strain gage.

False

Stress contours contain the information of direction of the principal stresses.

True

Stress trajectories contain the information of direction of the principal stresses

True

Tensor quantities in mechanics are stress, strain and moment of inertia.

first degree

The beam in the following figure is statically indeterminate to the

when the angle of rotation is small. linear elastic materials

The bending moment equation (EIv''=M), shear force equation (EIv'''=V) and load equation (EIv''''=-q) apply to (check all that apply)

True

The diameter of a Mohr's circle for plane strain is the same as the difference between two principal strains

True

The difference between two principal stresses (maximum normal stress - minimum normal stress) is equal to twice of the maximum shear stress in magnitude.

The area on which the internal pressure acts A The area on which the tensile stress acts B The volume of the half sphere C The surface area of the half spere D

The figure shows the half of a thin-walled spherical pressure vessel (radius r, thickness t). Match the areas on which the internal pressure p and tensile stress acting and other calculations.

True

The figure shows the half of a thin-walled spherical pressure vessel. The force due to internal pressure p acting on the left half (P) is equal to p*pi*r^2

True

The first moment-area theorem states that the angle between the tangents to the deflection curve at two points A and B is equal to the area of the M/EI diagram between those points.

True

The flexure formula, , which relates the normal stresses in the beam to the bending moment M, is based on the following assumption that the material is linearly elastic.

Surface A A1 Surface B A2 Surface C A3

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)

Force in +x direction a Force in -x direction b Force in +y direction d Force in -y direction c

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 in (b).

tl^2*tan(theta)

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.

True

The longer a column, the smaller the critical load for the column to buckle.

the longitudinal strain is zero along the neutral surface y is the distance from the neutral surface

The longitudinal strains due to bending (ex =-ky) vary linearly with y, check all correct anwers

True

The maximum compressive stresses in a beam occur either on the top or on the bottom surface, not on the neutral surface.

False

The maximum normal stress under axial loading occurs at .+/- 45

False

The maximum shear stress on the outer surface of a cylindrical pressure vessel is zero.

The presence of the deflections does not alter the actions of the applied loads

The method of superposition is a practical and commonly used technique for obtaining deflections and angles of rotation of beams. The principle of superposition is valid under the following conditions (check all that apply).

m^4 in^4

The moment of inertia of the cross-sectional area of a beam has the following SI and US units

are zero on the neutral surface. act along the beam's longitudinal axis. are positive in one side of the neutral surface and negative on the other side of the neutral surface

The normal stresses of a beam under pure bending (check all correct answers)

true

The out-of-plane strains are zero for the plane strain condition.

false

The out-of-plane strains are zero for the plane stress condition.

true

The planes of maximum shear stress occur at 45 degrees to the principal planes.

the maximum and minimumn normal stress.

The principal stresses are

False

The radius of a Mohr's circle for plane strain is the same as the maximum in-plane shear strain.

True

The second moment-area theorem states that the tangential deviation tB/Aof point B from the tangent at point A is equal to the first moment of the area of the M/EI diagram between A and B, evaluated with respect ot B.

True

The shear formula, , which relates the shear stresses in the beam to the shear-force V, is based on the assumption that the material is linearly elastic

positive

The shear strain is __________(positive, negative) if the angle between two positive faces is reduced.

True

The shear stress on the inner surface of a spherical pressure vessel is zero.

True

The shear stress on the outer surface of a spherical pressure vessel is zero.

True

The stability of a structure is increased either by increasing its stiffness or by decreasing its length.

True

The stress transformation equations derived for plane stress can be apply to any material.

True

The sum of the normal stresses on any two perpendicular planes is constant, that is,

True

The wall of a pressurized spherical vessel is subjected to uniform tensile stresses in all direction.

True

The wall of a spherical pressure vessel is under biaxial stress.

0

There is a cantilever beam AB. It was supported at A and loaded by several loads. After careful calculation, the area of the M/EI diagram is zero, that is, the positive part equals to the negative part. What is the angle of rotation at B?

True

Under suitable conditions, the deflection of a beam produced by several different loads acting simutaneously can be found by superposing the deflections produced by the same loads acting separately.

True

We have an overhang beam under evenly distributed load. Between the two supports, there is a point of inflection. At the point of inflection, the bending moment is zero.

Pa, MPa, GPa

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?

PSI, KSI

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?

m^4

What is the SI unit for the polar moment of inertia Ip.

N.m

What is the SI unit for torque?

lb.ft

What is the US unit for torque?

delta(ac)+delta(bc)=0

What is the compatibility equation that we can use for this statically indeterminate bar. Fig 2-16

deltaC=deltaS

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.

0.0777

What is the normal strain (%, 4 decimal points) under axial loading if the elongation is 7 mm and total length is 9 m?

True

When a bar is under tension, the maximum shear stress occurs at . The minimum shear stress occurs at when the tensile stress is applied.

The top surface has the maximum tensile stress.

When a beam's bending moment at one section is negative, which of the following statement is true?

The top surface has the maximum compressive stress.

When a beam's bending moment at one section is positive, which of the following statement is true?

633

When a problem states that it is a plane strain condition, one principal strain is 5 urad and the other principal strain is -628 urad, what is the maximum in-plane shear strain?

210

When a problem states that it is a plane strain condition, the shear strain is 2 urad, normal strain in the x direction is 4 urad and in the y direction is -206 urad, what is the maximum shear strain in urad?

0.0117

When a problem states that it is a plane strain condition, the shear strain is 4 urad, normal strain in the x direction is 3 urad and in the y direction is -338 urad, what is tangent of 2*(the angle of the principal strain)?

False

When analyzing combined loading, we use the Method of Superposition. This method applies to any material.

The member only has linearly elastic deformation so that Hooke's law applies.

When deriving the equation for change in length of an axially loaded member PL/EA , we have made the following assumption(s):

The materials is linearly elastic and the Hooke's law for shear applies.

When deriving the equation for the shear stresses in a circular bar under pure torsion (G is the shear modulus of the material, r the radius of the bar and q the rate of change of the angle of twist), we have used the following assumption

The angle of rotation is small.

When deriving the equation for the slope of the deflection curve of a beam , we have made the following important assumption

The angle of twist, phi, is small.

When deriving the equation to calculate the maximum shear strain, gmax, of a solid circular bar under pure torsion, we have made the following important assumption:

the proportional limit of the material as its limit.

When plotting the Euler's curve (critical stress versus slenderness ratio) of a pinned-end column, the critical stress has

False

When the slenderness ratio (L/r) is greater than the critical slenderness ratio (L/r)cr, the potential column's failure mode is inelastic stability limit.

The angle of rotation is small. The material is linearly elastic. The presence of beam deflection does not affect the action of the loads.

When using the Principle of Superposition (POS) to analyze beams, we have made the following important assumptions (choose all that apply):

The presence of beam deflection does not affect the action of the loads. The material is linearly elastic. The angle of rotation is small.

When using the Principle of Superposition (POS) to analyze beams, we have made the following important assumptions (choose all that apply):

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.

The Load and Resistance Factor Design

Which design provision was based on probability concepts?

True

if a solid bar is under uniaxial loading in the x-direction, there are no normal stress in the y- and z-direction. However, there are normal strains in the y- and z- direction if the Poisson's ratio is greater than zero.

maximum shear strain= rad angle of twist per length=rad/m total angle of twist=rad L=length m

match the SI unit of each term.