Hot answers tagged

9 votes

Determine the moment of inertia of a filled circular sector

Consider an infinitesimal element of area $r d\theta dr$ which is at a distance $r \sin (\theta)$ from the $x$ axis. Its moment of inertia is $r d\theta dr (r \sin (\theta ))^2$. The moment of ...
user avatar
  • 1,876
8 votes
Accepted

What are the principles (if there are any) behind the conservation of bending moment in frame analysis?

Well, such an equilibrium (be it of moment, or shear or axial force) is necessary for any static system, and can be trivially demonstrated with Newton's second law. For forces, that is the classic $F=...
user avatar
  • 13k
7 votes

is bending moment on roller supports at beams zero?

no. The change in moment is zero, as you can see on your plot. I think you can see if you imagine sectioning the beam slightly to the right of the support and constructing a free body diagram, the ...
user avatar
  • 979
6 votes
Accepted

Calculating moment of inertia for a hollow discontinuous circle?

Edit: There seems to be a much easier way I overlooked, which I'll explain. My first answer is kept below for reference. Your assembly consists of a small sector subtracted from a larger sector as ...
user avatar
  • 628
5 votes

Force required to rotate an object on a plane - moment of inertia?

Since the friction is not known, the torque to overcome that friction can't be known either. You therefore can't do what you want since the problem is under-constrained.
user avatar
  • 11.3k
5 votes

Question in finding the direction of forces in a truss

It doesn't matter if you "guess right" whether each member is in tension and compression. The important thing is that the forces at the ends of each member are equal and opposite, and write ...
user avatar
  • 12.5k
4 votes
Accepted

Determine the moment of inertia of a filled circular sector

Since you actually asked for the moment about the $x$ axis. Calculating the moment of inertia about the $x$ axis is a fair deal more complicated than calculating it about the $z$ axis as in my other ...
user avatar
4 votes
Accepted

polar moment of inertia for compound shape

Without looking up all the formula's for you, the approach to this problem is rather simple. Find the polar moment of a solid cylinder, and subtract off the polar moment of the holes. For the off ...
user avatar
  • 979
4 votes
Accepted

A way to calculate the magnitude of the moment

This is a trigonometry question. Point B is a certain distance upwards from Point A. How much? You know the distance that it is to the left from Point A ($2\text{m}$) and the angle that it is from ...
user avatar
3 votes
Accepted

Sheet Metal Bending: stuck on calculating the minimum radius required

I hope the following helps. This is from a book I used in college. Manufacturing Engineering and Technology, 5th Ed. by Kalpakjian and Schmid Minimum Bend Radius ...
user avatar
3 votes

Moment of force or torque

A moment has a direction, which you can imagine when you look at the direction of the force and the axis you're calculating the moment from. Depending on which direction you're looking at it from, ...
user avatar
3 votes

Calculating the moments due to reaction forces on a bent beam

The reason is that both the horizontal and the vertical component of $N_B$ generate a moment around $A$. Since the moment due to a force is equal to the product of the force and the perpendicular ...
user avatar
  • 13k
3 votes
Accepted

Flexural modulus for a beam fixed at one end

The fundamental beam equation is $$\dfrac{\text{d}^2}{\text{d}x^2}\left(EI\dfrac{\text{d}^2w}{\text{d}x^2}\right) = q$$ Which basically translates to "the fourth derivative of the deflection ...
user avatar
  • 13k
3 votes
Accepted

Transfer of moments in beams with internal hinges

Imagine if AB didn't exist, so all we have is BD with the pinned support at D and the force at C. In this case, BD is hypostatic and becomes a mechanism, rotating around D. Obviously, we know that ...
user avatar
  • 13k
3 votes
Accepted

Why is the bending moment equation for a uniformly distributed load (w) across a length x on a structure given by w(x)(x/2)?

consider an infinitesimally small section of a beam from coordinate $x_1$ to $x_1-dx$ loaded with a distributed load w. The moment of this load about point $x=0 \ is \\ M= w*x*dx.$ Now if we have ...
user avatar
  • 21k
3 votes

Does the turboprop engine torque get transferred to the engine mount and ultimately aircraft when engine is active?

For every action there is an equal, but opposite, reaction. Never found a case that this is not true. Torque reaction on the P51 even caused uneven tire wear: https://www.aopa.org/news-and-media/all-...
user avatar
  • 14.1k
3 votes

Is bending moment along a beam independent of the cross sectional area of the beam?

You seem to be mixing up a few concepts. As others have mentioned, bending moment is independent of a structure's cross-sectional dimensions. After all, bending moment is simply the sum of $F_i\ell_i$,...
user avatar
  • 13k
3 votes

Torque for servos of tiltrotors

If we ignore the effects of changing the angle of the rotor causing changes in lift and as a starter point to give us a basic idea of how to rotate the axis of the tilt-rotor. Let's assume your rotor ...
user avatar
  • 21k
2 votes

Different measured strain in beam experiencing pure bending

I would add to the above answers: The beam could have sustained strain hardening from the manufacturing, cutting, preparation or any strain history that has left local changes in its elasticity ...
user avatar
  • 21k
2 votes

Different measured strain in beam experiencing pure bending

If the loads you apply are too big, you can get local crushing of the beam, or plastic deformation of the beam at the loading points instead of uniform elastic bending. But without more details of ...
user avatar
  • 12.5k
2 votes

Different measured strain in beam experiencing pure bending

What variation in value are you experiencing? Theoretically, the curvature or strain of the beam should be constant in between load points. Minor variation could be expected, but major probably ...
user avatar
  • 66
2 votes

Flexural modulus for a beam fixed at one end

'I' doesn't change for the different situations. 'I' is a property of the cross-section of the beam - a rectangle of width w and depth h. The Eb equations are correct for the situations set out, with ...
user avatar
  • 622
2 votes

Moments of inertia, rods mechanism

The point where center of mass lies so the center of gravity. So, for center of mass For rod AC. B is the mid point of AC.So,let us take A as origin So coordinates of B($\frac{l}{2}$,0).Similarly for ...
user avatar
2 votes
Accepted

Maximum torsion shear stress in cylinder

I have not repeated your maths, but the formulae are shown in the image. If you have the numbers correct the you have a shaft that will support nearly 5 times the load you are applying... Source : ...
user avatar
  • 14.1k
2 votes
Accepted

Second Moment of Area for slanted triangle?

Oscar, I'm not sure what your math background is, but there are a lot of different ways to get there. The most direct is to just reason from the properties of affine transforms, specifically shear ...
user avatar
  • 3,590
2 votes
Accepted

Is radius of gyration same for both types of moment of inertia?

Area moment of inertia and mass moment of inertia are two different things. A) Mass moment of inertia (or moment of inertia): This is the resistance offered by a solid body when subjected to ...
user avatar
  • 1,423
2 votes

is bending moment on roller supports at beams zero?

Bending moment is the area under the shear diagram which is definitely increasing by a slope of 5kn/m as it gets closer to support in a straight line, so it is maximum on the support. And this moment ...
user avatar
  • 21k
2 votes

Calculating moment of inertia for a hollow discontinuous circle?

very close to 1E-3 in^4 More precisely: 997E-6 in^4 I wouldn't (didn't) use either of the other algebraic proposals. It's relatively easy to write an equation for the width of cut face at a defined ...
user avatar
  • 622
2 votes

Skewing of joints using virtual work

Let's assume that in equilibrium the links 1 and 4 will be at angles $\theta_1$ and $\theta_4$ with the vertical. The relationship between these angles can be determined from the fact that the ...
user avatar
  • 1,876
2 votes
Accepted

Transfering moment through internal hinge

"Hinges don't transfer moment" is just a way of saying that hinges do not resist bending, and therefore suffer no bending moment. You can basically "translate" that term as "Bending moment at hinges ...
user avatar
  • 13k

Only top scored, non community-wiki answers of a minimum length are eligible