What is Mechanics of materials: Definition and 103 Discussions
The field of strength of materials, also called mechanics of materials, typically refers to various methods of calculating the stresses and strains in structural members, such as beams, columns, and shafts. The methods employed to predict the response of a structure under loading and its susceptibility to various failure modes takes into account the properties of the materials such as its yield strength, ultimate strength, Young's modulus, and Poisson's ratio. In addition, the mechanical element's macroscopic properties (geometric properties) such as its length, width, thickness, boundary constraints and abrupt changes in geometry such as holes are considered.
The theory began with the consideration of the behavior of one and two dimensional members of structures, whose states of stress can be approximated as two dimensional, and was then generalized to three dimensions to develop a more complete theory of the elastic and plastic behavior of materials. An important founding pioneer in mechanics of materials was Stephen Timoshenko.
If there is an axial load on G the centroid and i want to calculate the stresses at point B , I will calculate the moments at point B then use the stress formula. I am confused as to what y and z is in this case. I know that y and z are the coordinates of the point that i want to calculate the...
TL;DR Summary: A frame with a triangular distributed load is pin-connected to a 2-force member. Find the combined stress at point E on the frame.
I am stuck at determining the value of M at the cut. The book shows the value at 8.25KN-meter, but I cannot see how they arrived at that number...
Anyone know of any book on mechanics of materials that covers finding the core of a section in eccentric loading. I am not sure what the term is in english but the direct translation is core of the cross section, it is the region in which if a load is applied, there will be only tensile or only...
Does Poisson's ratio apply when we have no loadings ? For instance if we have a free rod and we increase its temperature, in order to find the change of its diameter should i say :
Δd=-v*ε_x*d, where d is the length of the diameter or Δd= α*ΔΤ*d ?
Thanks in advance.
I have a couple of questions about pressurized vessels. They're not completely related but since they're both about a similar topic I thought it'd be best to discuss them in a single thread. I'll be talking about a pressurized sphere (absolute internal pressure > 0 & absolute external pressure =...
Im so confused on these solutions here for the shear stresses. Why is Tau_V sometimes negative and sometimes positive? Can someone please explain this and maybe illustrate?
Here for example.
Heres the solution for problem b):
Here Tau_V (talking about F_xQ/(Ir) ) is negative, so how im...
Hi, i'm struggling with that problem , i need to find the distance that point N went down.My way of thinking is that the structure is twice not statically determined because of the beam MN and beacuse of the left support which is also unnecessary in order for equilibrium. My 2 equations of...
How can I find the maximum bending moment and maximum deflection for a spring?
It would be very helpful if you could explain the specific procedure and formula in an easy-to-understand manner.
that's all, thank you very much.
Summary:: Torsional stress on freely spinning shaft?
Hey guys,
I’m having some confusion with a certain section of the “Torsion” chapter in my mechanics of materials book: “power transmission”.
Please see the problem below. This is very easy to SOLVE (basically plug and chug with the...
Hello!
I am new to mechanics of materials and I am very confused about the problem below. So the shear formula is:
tau = VQ/It
From the book (Hibbeler) I understand that Q is "y'A', where A' is the cross-sectional area of the segment that is connected to the beam at the juncture where the...
Hello. I am reading Hibbeler's Mechanics of Materials (ninth edition). Example 7.5 computes shear flow at a segment where there are nails attached to different boards.
He chooses a cut like the one shown here:
And gets (by symmetry between C and C') the shear flow q computing the first moment...
For quasi-brittle materials, there is an energetic size effect as well as a statistical size effect, as described here. However, it seems to require a stress gradient for it to play a role, as in the example given with a 3-point bending test. The stress at the middle of the fracture process...
For the second one I thought I'd find the shear max caused by the first torque, and use the value as my radius in Mohr's circle, then proceed to find the stress and shear caused by the new torsion and moment (in terms of M), and proceed to use the criteria to solve for M. I seem to be going in...
My question is simple. Why do we need 9 different quantities, ie 1 normal stress and 2 shear stresses on 3 different planes, to define stress at a point?
example: http://www.geosci.usyd.edu.au/users/prey/Teaching/Geol-3101/Strain/stress.html
I think it should be enough to define the 3 stresses...
am Samuel Owino, a software engineer for the Institute of Biomedical Informatics Research in Eldoret Kenya. I look forward to contributing to the growth of the forum.
cheers!
Homework Statement
Knowing the left lug is carrying 10,000 lbs, determine the loads P1 and P2 in the lugs on the opposite side of the pin.
Homework Equations
Force Balance (ΣF=0)
Another equation needed
The Attempt at a Solution
10000 = P1 + P2
This is where I need another equation to...
Homework Statement
Consider 2 balls A,B on the same line . and they are connected to a third one G with a rope L. AG, AB. now the system monves in the effect of the mass of G and its projection to the line AB is in the middle. No friction. mass of A=mass of B=m and mass of G=2m
.FInd the time...
Homework Statement
Find reactions at ends and deflection at C
Homework Equations
RA + RE = 115kN
##\delta##Total = ##\sum## (PiLi)/(AiEi)
The Attempt at a Solution
RA + RE = 115kN
Then apply superposition: (Get rid of RE) divide whole member into 4 elements and add.
##\delta##Total =...
Homework Statement
Homework Equations
G = Shear Stress/Shear Strain G = E/(2(1+n)) n being poissons ratio
The Attempt at a Solution
So I know the easiest way to solve is simply to manipulate the first equation a little bit >>> Shear Stress = G * Shear Strain >>> Shear Stress = P/A >>>> P...
Homework Statement [/B]
The inclined ladder AB supports a house painter (85 kg) at C and the self weight (q = 40 N/m) of the ladder itself. Each ladder rail (tr = 4 mm) is supported by a shoe (ts = 5 mm) which is attached to the ladder rail by a bolt of diameter dp =8 mm.
1) Find support...
Homework Statement
Homework Equations
Torque = F. d
Distributed Force -> Concentrated Force = w.d
The Attempt at a Solution
Concentrated force is equal to 40kN and I have found the B(y) as -10kN by taking moment with respect to the A point. And from the equilibrium A(y) is 50 kN...
Hello guys. In the picture below can u help me with the problems! I cannot understand what exactly should I comment about the strengths. I t would be easier if it was asking about the types of welding :) . Please give some help! Thanks in advance!
Homework Statement
Homework EquationsThe Attempt at a Solution
I feel I did something wrong, but not sure where is my problem. I don't feel conformable on number 26 and 27 and 29, can someone please tell me which answer is incorrect and any tip on solving it would be greatly appreciated!
Homework Statement
Homework EquationsThe Attempt at a Solution
I am a little confused by the wording of the textbook solution.
from the solution, the displacement at the end C of the rod = the displacement of C relative to the fixed end A,
why not the displacement of C relative to the fixed...
Homework Statement
The stress distribution along the section of a bar is shown below. From this distribution, find the approximate axial force P in kip.
Homework Equations
δavg=P/A
A= (.6+.6)(.5)
δavg=30ksi[/B]The Attempt at a Solution
P=(30ksi)(.6in2)=18kip
It says this answer is wrong...
Homework Statement
The 40 ft long A-36 steel rails on a train track are laid with a small gap between them to allow for thermal expansion. Determine the required gap in inches so that the rails just touch one another when the temperature is increased from -20 F to 90 F. The cross sectional...
Homework Statement
Hi! So my question isn't really about a specific problem, but more of when to use which method.
I'm having trouble knowing when to use the method of super position, the force method, or just being able to go straight into just writing the equilibrium equation and the...
Homework Statement
Calculate the weight of each member of the truss structure.
Homework Equations
density = mass/volume
The Attempt at a Solution
This is part of a lab that we are doing in my mechanics of materials course. I have designed a structure, and I must calculate the weight of each...
Homework Statement
Homework Equations
Equation of Equilibrium (Horizontal and Vertical Forces, Moments)
Normal Stress = F/A
The Attempt at a Solution
I have already solved the solution for this problem. For part (a), I simply found the force in the link, and used the cross area where the...
I am learning about shearing stress, and I am a little confused about the area of projection mentioned in my book. When it introduces it, it shows a plate with a rivet through it. The plate is of thickness t, and the diameter of the rivet, d. It shows the plate and the rivet cut in half by a...
Hallo,
I Wonder how i can get the equation of motion for a tilting Stick of mass M and lengh L with an additional mass m placed in it in distance of l from the Center of rotation.
I thought about the moments of inertia
Can anybody help?
Thanks in advance
Hello guys,
I am a 2 year B.E student in mechanical engineering. I like solving mechanics of materials, math parts veru well( excerpt numerical methods). Reading and YouTube ate my favourite hobbies. Nice to meet you
If a rod is in compression, will the minimum area on rod ( the section where there is a hole for pin) stress free? What if the rod is in tension? The rod BC is in compression and the boom AB is in tension?
http://imgur.com/a/6asfB
Good evening. I've got stuck in this question from my book of Mechanics of Materials by Beer and Johnston about torsion.
The allowable shearing stress is 15 ksi in the 1.5-in.-diameter steel rod AB and 8 ksi in the 1.8-in.-diameter brass rod BC. Neglecting the effect of stress concentrations...
Homework Statement
I have to solve for Ay, By, and Cy reaction forces. The constant C is a couple acting at A in a clockwise direction Homework Equations
Sum of all forces = 0
Sum of Moments about any point = 0
The Attempt at a Solution
I solved for all four reaction equations(one force sum...
Homework Statement
A flat part with constant thickness b is loaded in tension as shown. The height changes from 50 to 87 mm with a radius r = 4.0 mm. Find how much lower a load can be transmitted through the bar if the height increases from 50 to 100 mm and the radius increases from 4.0 to 10...
Homework Statement
Homework Equations
δ = Pl/AE
σ = P/A
The Attempt at a Solution
I had calculated the deformation for both the steel and aluminum, and added them together to give me δ = 0.481 mm, which is incorrect. I also thought I could simply plug in the force P = 200kN and the...
I conducted a uniaxial tension test for a variety of materials but wasn't able to gather much useful axial strain data due to the extensometer continually slipping. I have axial strain data for the linear elastic region of the stress strain curve and I also have the extension of the crossbar of...
Homework Statement
Hollow Circular tube of Length (L) 600 mm is compressed by forces P (axially).
Outside diameter (d2) is 75 mm.
Inside diameter (d1) is 63 mm.
Modulus of Elasticity (E) is 73 GPa
Poisson's ratio (v) is 0.33.
axial strain (ε) is 781 x 10-6
Find shortening of tube (δ). (This...
Homework Statement
http://prntscr.com/7rtrep
http://prntscr.com/7rts95
Homework Equations
theta = TL/GJ
t(max)= Tc/J
The Attempt at a Solution
The two questions i have are rather similar so i put them up at the same time, i hope that's okay.
For the first one ( the first link) i started by...
Homework Statement
Hi there.
I have to do this excercise for my exam and I am kinda lost with the verification of data, more precisely calculations. Can you guys help me out?
I set 100N load right above the hole... the distance between centers of the hole and nut is 190mm. the max distance...
TERMS:
Slip Plane: is the plane that has the densest atomic packing—that is, has the greatest planar density.
Slip Direction: corresponds to the direction in this plane that is most closely packed with atoms—that is, has the highest linear density.
NOMENCLATURE:
θ = angle of the slip plane as...
Homework Statement
Actually I have two doubs, the first one is Why in the solution of this problem, in the sumatory of moments in C, Force 2=10?? If in the sumatory of moments in F, Force 2 is 416.7 N. Actually I calculate with 416.7 N, and T in C = 100 N. The other doubt is with the sign...
Homework Statement
How can I calculate the ultimate stress? (I refere to the stress that it's in the green rectangle). I have a real graphic, I have two deformations, (it was 2 test, from the same material) and only one stress. The orange curve is Stress versus unit deformation 1, and the gray...
Homework Statement
Calcular the force P when a bar starts yield, when 2 bars start yield, and when the 3 bars start yield
Diameter = 25 mm (for every bar), Yield Stress of Steel = 250 MPa.
Homework EquationsThe Attempt at a Solution
[/B]
[F][/AD] + [F][/BE] + [F][/CF] = P
2[Δ[/AD] -...
Homework Statement
Homework Equations
Area AD = Area BE
E(AD) =E (BE)
Yield stress = 250 MPa[/B]
The Attempt at a Solution
Delta= PL/(AE) if in both bars the A and E are the same, and from the equilibrium I get Q= 4.125 F(AD) + F(BE) , also from the compatibility I get delta AD = 4.125...