What is Strength of materials: Definition and 40 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.
TL;DR Summary: What would be the strongest material such pair of rods be able to punch through if the bottom of the rods was at 200 m from sea level and a platform with the strong material was at sea level, with 88,110 Kg on top of the rods?
The following is just for fun, it doesn't need to be...
I have tried solving this by splitting the load into two parallel coplaner loads as the Hint below the question suggests but while i was computing the values i realized that, i'll have 4 variables with only 3 equations.
two forces and the two distances to forces from their respective axes.
i've...
In every book I checked, the energy (per unit mass) of elastic deformation is derived as follows:
## \int \sigma_1 d \epsilon_1 = \frac{\sigma_1 \epsilon_1}{2} ##
and then, authors (e.g. Timoshenko & Goodier) sum up such terms and substitute ##\epsilon ## from generalised Hooke's law i.e.
##...
I am working on a project where I am supposed to find some ways to get constraints on some of the components (rim, hub and spokes) to use these for parametrization. So far I have thought that the constraint for the rim is that it can't buckle from the pre tension of the spokes (here I am...
Hi,
So,I'm helping a guy with his mechanical engineering homework.
The problem is that the guy is so off, he doesn't even know the name of the subject.
And honestly, I having a hard question finding out what this question is about.
I need to proove the Zb=h^2/3 thingy. I have no idea what this...
Hi everyone, I am new here, so please be kind if I make mistakes on this forum, I will try to learn fast.
I need help in explaining the solution of one of the examples from Timoshenko's Strength of Materials book. The solution is provided in the book, but I did not get it, no matter at which...
Hello smart physicists!
I'm hoping to run a span of 124" for a pull up bar, with a support in the middle at the 62" point (so 3 supports total). I'm using the Rogue P-5V Pull-Up Bar Brackets (https://www.roguefitness.com/rogue-p-5v-garage-pullup-system). The brackets call for a tube with a...
Homework Statement
https://ibb.co/imui5b[/B]
hey i need to calculate max normal stress at BC and max shear stress at b and c
is my torque equation right?
Homework EquationsThe Attempt at a Solution
so i thought
Σma=0 Cx*6+80*6+80*2=0
i ll find cx
and then ΣFx=0
and ΣFy=0
I have a 30 by 30 pole barn type garage that is my workshop where I am trying to restore an old 68 Mustang of my grandfather who passed away. The trusses are 2x4 and are four feet apart. My thinking was to create a beam that runs perpendicular to the trusses about 10 to 15 feet from the edge...
In mechanical engineering we have various courses in strenght of materials, and I've noticed that graduate students learn the Theory of Elasticity. I've researched a little bit about it, and I know that the Theory of Elasticity is more general than strenght of materials. But I have some doubts...
I am currently re-fabricating solar concentrator dishes to allow for automatic tracking of the sun during the day and month. The industry term for these dishes is 'CSP' (Concentrated Solar Power).
Task at hand:
The CSP parabolic dishes are currently manually adjusted to the position of the sun...
Hello All,
First off great forum; lots of useful info on here. I was wondering if anyone had any experience or could refer me to a text regarding the tensile strength of polyhedrons? I am experimenting using various types for a super strong mechanism to aide manufacturers during metal...
Ive been trying to work out these problems for 2 days now. I've read through the book "Statics and Strength of Materials, Second Edition" By: Cheng. I've googled Everything. I've been on other Forums and have got no reply. I've tried Facebook Math Pages. No Answers. I've been Looking for free...
Homework Statement
Member AD of the timber truss (shown in attachment) is framed into the 100 x 150 mm bottom chord ABC as shown in the insert. Determine the dimension "a" that must be used if the average shearing stress parallel to the grain at the ends of chord ABC is not to exceed 2.25...
A propeller shaft in the largest and most powerful ships transmits about 50,000 hp (1HP=33,000 ft*lb/min). Assume that the propeller transforms this power into a forward push on the ship with an efficiency of 70 per cent and that the ship's speed then is 30 knots (1 knot is 6,080 ft/hr).
The...
Hi, all I have to do a project but I need some guidance. I have to make MATLAB draw bending
moment and shear force diagrams of a beam which have to be loaded with a distributed load,
a single force, and a single moment. First I have to make MATLAB draw a beam like in the picture.
1. Calculate the forces in the members FG, GD, and CD of the truss shown in the figure by using the principle of virtual work. All horizontal and vertical members are 1m long
2. I have attached the diagram
3. I can easily calculate this using normal principles, but not understanding how to use...
I'm working on a problem but I've hit a road block..
Then the cross section of the piece is here:
The first part of the problem is to determine Iy, Iz, and Iyz of the member.. I found the y value of the centroid to be 2.8587" and the z value of the centroid to be 1.0734" using the...
A mild steel solid shaft is to be replaced by a stainless steel hollow shaft of the same
outside diameter. Calculate the ratio of internal diameter to external diameter of the
hollow shaft for equal strength. Also find the percentage saving in weight if density of
mild steel is the same as...
Consider a cantilever beam of rectangular cross section made up of two materials steel and aluminium. an axial force is applied at one end. the question asked was which material should make up the upper part and which should make up the lower part of the beam?
Could someone please help me in...
Homework Statement
QUESTION 2 (Total 20 marks)
Figure 4 below shows a diagrammatic section of the floor of a typical house suspended over a garage. The steel beam shown in section spans 7.2 metres centre to centre of supports. The floor, including an allowance for the self weight of...
Homework Statement
I am having trouble with question 1 on the attachment posted. I understand that i need to get the area of the 2 bars. I am just not sure what to do with the forces. ALso i know the picture may be dark. P2 starts at point B and is pulling to the right and P3 starts at...
I have a scientific background in materials science. However this is one type of material that we don't exactly learn about!
Let's say you have a neutron star approaching a comparable mass black hole. As the neutron star approaches the event horizon for such a comparable black hole, tidal...
A bar of length 4m when used as simply supported beam and subjected to a uniform distribution load of 30kN/m over whole span, deflects 15 mm at the center. Determine the crippling loads when it is used as a column with following end conditions.
a)both ends pin-jointed
b)One end fixed and other...
R at B = 5.0625
R at A = 8.5kN-5.0625kN=3.4375kN
x/0.9375=(0.5-x)/4.5625
x=15/176
but moment near x there i get different from both side:
from A = 2.431kNm
from B = 2.346kNm
is there something wrong?
Homework Statement
1. Prove the equations.
2.Two solid circular shafts are connected by 5cm and 25cm-pitch-diameter gears as shown
in Figure 1.2 below. The shafts are assumed to be supported by bearing, as such bending
is negligible. Find the angular rotation at end D with respect to end A...
Homework Statement
The bars in the truss each have a cross sectional area of 1.2in^2. If the maximum axial stress in any bar is not to exceed 25ksi, determine the maximum magnitude of P of the loads that can be applied to the truss. Determine the elongation of each member.
E=29,000 ksi...
Here are some great Strenght Of Materials problems..
Scroll down and under the coursework problem click the example and take a look at the different problems.. Those are fully solved.
I'm not sure how long the site will be active but its very helpful so download the pdf file before my professor...
in general, do ductile matreials fail due to shear or tensile stress
i think that my lecturer said that brittle materials (such as concrete) will fail due to a low maximum shearing stress therefore breaking at 45 degrees in axial loading, and ductile materials have low tensile stress leaving...
Homework Statement
A rigid steel plate is supported by three posts of high-strength concrete each having an effective cross-sectional area A =40000 mm2 and length L = 2 m. Before the load P is applied, the middle post is shorter than the others by an amount s = 1.0 mm.
Determine the...
Hi
I wonder if you could help a really thick oldie with a problem, I found this:-
I need to build a set of ramps for my dump trailer. The ramps will be
6' long. I have and want to use 1" x 3" 11 gauge rectangular steel. If
I were to take one 6' piece of this material, stand it on its'...
Seatwork no. 1 -------Strength of Materials----------
The 20 mm diameter bolt fastens two wooden planks together. The nut is tightened until the tensile stress in the bolt is 150 Mpa. Find the smallest safe diameter “d” of the washers, if the working bearing stress for wood is 13 Mpa...
Knowing the portion of the link BD has a uniform cross-sectional area of 800mm^2, determine the magnitude of the load P for which the normal stress in that portion of BD is 50 Mpa. (Hint draw a free body diagram of the link ABC)
http://img137.imageshack.us/img137/9845/problmezf4.png
sorry for...
Homework Statement
In the attachment
Homework Equations
The Attempt at a Solution
I have been solving this question for quite some time but I can't get the answer yet.
I offset all the forces to point C and I get the following values:
Moment at y-axis, M(y) = 10Nm
Moment at...
if anyone could provide any insight as to how i go about completing this question i would be grateful, i was off the week this was taught to the group and have no idea whatsoever
Can anyone help me understand the concept of a "strain invariant" given a strain state matrix? or perhaps point me towards something?
thanks for any help.
Im including a scan of the problem and my work, please let me know if I did this right. Sorry about the sloppy handwriting.
http://img244.imageshack.us/img244/6521/strengthsproblem3rk.th.jpg
http://img241.imageshack.us/img241/8866/strengthsworkedout1rw.th.jpg
http://physics.uwstout.edu/StatStr/Strength/indexfbt.htm#STATICS%20&%20STRENGTH%20OF%20MATERIAL
The above link has become inactive (the author, Robert Foley has apparently retired), but another professor has put the course notes into a pdf...
While mowing the grass, I thought of the following problem (to take my mind off of the heat!)
Consider a vertical column of water in a container. The pressure exerted by the water on the sides of the container is rho x g x h, where rho is the density of the water, h is the height of the column...