Structural Mechanics
Hi guys this is my first lecture on the structural mechanics in this lecture we'll be covering on the basics and then we'll go forward accordingly so let's begin our journey to structural mechanics yeah so what is structural mechanics well all structures are designed for some specific purpose whether it is simple or complex but they must be capable of carrying the loads that they are designed for without collapsing right so while designing or analyzing
these structures what are the basic terms that you are going to keep in mind well first one is forces and moments then second one is types of forces and the deformations because of that force then third you need to check whether the system is in equilibrium or not then what are the stresses developed in the system and then what are the corresponding strains and these are the basic terms that we are going to discuss today so you know whenever any material is subjected to external load and deforms it changes its shape due to the application of force or change in a temperature
you know like material expands and contracts whenever there is a variation in temperature you all must have experiences life experiences thing in your daily life so mechanics of material
rotation there are different type of constraints and we will study about them in our second video lecture now what
allows earth to predict the deformation in the material using which we can predict the failure of structure as you can see in an
Example:
given the stop the structure is subjected to various loadings and constraints at some locations so what do you mean by constraints constraints are like something you can say hold this structure like if you talk about cantilever beam fixed and is constrained there will be no displacement on
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happens when we apply external force to any object it reduces internal forces
okay and these internal forces will led to the deformation of the body so now stresses are set up in the body and though and so the corresponding strings and by using these stress and strain relationship weaker we will protect the failure of the object so these all these things will come under topic off theory of failure since this is the first lecture.
I am just giving me
the brief for everything we'll discuss everything in detail we will now see the type of forces
well the first one is external force so by the name itself you can say that these are the forces caused
by the external agent outside of the system now it can include applied force normal force tension force or a friction force or air resistance force correct now if your load is concentrated on one point or acting on one point only it is said to be concentrated load but what do you mean by acting on one point it simply means say the contact area is very small and so we say that it is acting on a point after this comes port
forces this you know from very beginning of your engineering that the force is due to gravity electric fields and magnetic fields are body forces so we can conclude that the body force is a force that act throughout the volume of the body next type of forces is surface closed surface Laurens that is applied on surface example pressure load pressure load is is a surface mode then line load water line loads these are the loads that act along line like this for
example
the weight of the partition
resting on the floor it's a typical example
Now next internal forces internal forces are forces exchanged by the objects in the system these are the forces which hold an object together when external forces or let's say loads are applied let's take an example on this part when you are applying a force F on this bar internal forces which you can see they are distributed come into these forces will resist the movement on its elongation of the bar okay so these are window
then
you know has already discussed that whenever load is applied it leads to the deformation of an object when you apply load in an axial direction then it will deform into axil direction it can be a tension or it can be a compression so accordingly it will elongate or it will short it it will get shot that that depends on what type of force you are applying okay when you apply force parallel to the cross section like shown in the figure it will deform and that deformation is measured as the total angular change in radians at the corner right similarly when we
when you apply it to sting force it will also result into angular deformation but what is the difference between both the deformations the differences like shear force will lead to in-plane deformation and twisting relate to the out of plane deformation bending moment it bends the beam it it will elongate the one surface after applying forces all we need to check is
whether the system is in Equilibrium or not so when you will say that the body is in equilibrium well the body is said to be in equilibrium and the resultant of all forces and movements acting on it is zero so first one is resultant of all forces must be zero and the resultant of all movements about any point must be zero so you can take any point and just find the resultant of all the moments about that point it should come and zero we have an example here here force P R P is acting at an angle on the free side of the beam so to be in equilibrium force P will act at the fixed position but in the opposite direction this is the solution
this topic and our second door and I think third lecture then to investigate the internal resistance of a structure the most famous method is a method of sections consider a single bar that is under tension and take a curve at any cross-section to see the internal forces now a bar is divided into two parts now separate each part then by using equilibrium of force the folds on curved
section must be equal to F similarly the force will be acting on the left face but also in the opposite direction
so we'll discuss some solve questions on
Stress
Now our next topic is Stress well if you'll go by the definition of the mathematical entity stress is nothing but the force divided by area that the force acts upon but this is not at all no like this is not all stress is of physical quantity that expresses the internal forces that neighboring particles of a continuous material exert on one another so we have two type of stresses normal stress and then we have shear stress now check this example the ex-seal force produce a uniform stretching of the bar hence the bar is set to intention as you can see as you can see in the figure now to investigate internal stresses produced in the bar we will make a imaginary cut section at m m and nm
Since n n cross-section is near to the load it will result in high localized stresses and non uniform stress distribution over cross section in the vicinity of the load as we move away from the end that is towards mm the stress distribution generally approaches the uniform distribution so what we do is we generally take the average of stress as you can see in the figure this one FS is also producing shear stress on that face as forces parallel to the cross section okay
Strain
Now comes the in Strain strain is a measure the deformation of the material normal force will either elongate a bar or contracts a bar and that depends on the nature of force and corresponding strain we normal stream so here if you're applying a force F so your length is changing from L to L plus Delta L so what is the increment in length it is
Delta L so Delta L divided by L will be your normal strain similarly we have shear strain so when a shear force is applied the body will deform and the measure of the change caused by the stress in the in the right angle between the two fibers within a plane you can see the figure here so this is a rectangular box fiber one and fiber to so when you are applying a shear force on this you can see how it is getting distorted so our total shear strain will be alpha 1 plus alpha 2 this is all for the first lecture thank you for your attention and you can proceed with the second lecture thank you.
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