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What are the units used in beam bending equations? Do they matter?

Yes, the equations are valid for both imperial and metric systems. The most important thing is to use consistent units of a system throughout the calculations. Consistency of units matters as most ...
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Limits of Euler-Bernoulli Beam Theory for Wide Plate in Flexure?

For a rectangular simply supported plate with length $a$ and width $b$ (Roark's Formulas for stress and strain): $$\sigma_{max} = \sigma_b= \frac{\beta qb^2} {t^2} $$ $\beta$ ranges from 0.287 for a=...
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Why do we always need to calculate the 'Moment of Inertia' about neutral axis for bending?

The derivation for bending stress is depended on the assumption that the strain distribution across the thickness is linear. i.e. $$\epsilon(z) = a_1 z + a_0$$ where: $a_0$ $a_1$ are coefficients of ...
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4 votes

Why do we always need to calculate the 'Moment of Inertia' about neutral axis for bending?

Because we're not interested in the moment of inertia or the "c" ordinate of a particular area element of the beam for their own sake - we're interested in them as intermediate steps on the ...
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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 $F_i\ell_i$,...
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3 votes

Does the Superposition principle actually make sense in reality for a rod subjected to bending and axial force togehter?

In setting small-angle deformations as a limit we set the limit for strains in all configurations to be elastic and totally reversible. Meaning if the beam deflects under the load or twists under the ...
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Does the Superposition principle actually make sense in reality for a rod subjected to bending and axial force togehter?

The superposition principle is valid if the assumptions it makes are valid. A commonly used set of valid assumptions are small displacements and strains and linear elastic material behavior. For large ...
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How to plot bending moment diagram from shear force diagram

First of all the bending moment, according to the usual convention (and the one you are presenting here) is positive. However, the problem originates when you add the area of the shear force. (...
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3 votes

Stress Concentration Factor – Why a Specific Range?

From what I see, in this picture from the Shigley book, if I really had to, I would extrapolate to 0.5 (or more precisely interpolate between the limit cases). The limit cases for very thick plate (d/...
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3 votes
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Why can't I-beam resist torsion but can resist shear stress due to transverse loading?

IMHO the most important issue, is that the IPE cross-section is considered an open section with respect to torsion. This reduces the resistance to torsion significantly. Figure : Shear stress due to ...
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2 votes

Elastic thin hard material with dog nails scratch resistant

If you are using the term "elastic" to means something flexible and not necessarily stretchy, consider that leather is a good choice. Leather can be bonded to wood using mechanical means (...
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2 votes

Bending stiffness of composite shaft

The bending stiffness will be determined by the second moment of area ($I$). The formula you provide $\int\int r^2 da$ is for the Polar Moment of area ($J_p$), and is valid for torsional problems. ...
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2 votes

How does Nonlinear Viscous Damping work? In what way are Viscous Dampers typically nonlinear?

The following graph shows you the properties of Polypropylene at high strain rates As you see here the modulus increases with increasing displacement rate (its not entirely equal to strain rate but ...
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2 votes

BMD of the beam joined at intersection

If you are an engineering student, you understand that beam deflects under load, and the longer the more flexible than the shorter beam, thus deflect more. The answer to this problem can be worked out ...
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2 votes

What are the units used in beam bending equations? Do they matter?

What's an equation? In life there are two types of equations: theoretical equations are obtained from first principles: make some assumptions and then play around with variables until you get a ...
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2 votes

What are the units used in beam bending equations? Do they matter?

SI In the SI, you are correct that the idea is that you don't need to modify the equations. You can use any units in the equation and perform the conversions in the calculation. Typically, what one (...
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2 votes

How to calculate the deflection displacement of a circular looped, closed bending beam?

Since the ring is welded to the support posts. Assume the assembly is stable, the posts are non-yielding nor buckling, and the welded connections can be assumed fixed. Then you can use the solution ...
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2 votes
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Justification of static equilibrium for a cut structure/frame

For your first question regarding whether the shear in BC equals the shear in DE: yes, they are the same. An easy way of seeing this is that some fraction of $P$ is going to be absorbed by BC as shear,...
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1 vote

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

A bending moment is an external moment that does not have anything to do with the section or material properties. Let's say we have a concentrated load applied at the center of a simply supported beam....
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1 vote

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

Yes, the load is independent of the cross-section of a structure in the example you are quoting and for most cases that an engineer would meet ( wasabi had the patience to write a detailed and more ...
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1 vote

Metal sheet forming - material properties when switching material

Springback will mostly be controlled by yield strength. And because all three materials have the same minimum yield (140 Mpa), the only option is to bend samples. You could get identical results with ...
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1 vote

Shear and Bending Moment

If you are only interested in approximation, the inner tube can be considered as a clamped cantilever after getting in contact with the walls of the outer tube, thus the applied load is resisted by ...
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1 vote

Find the maximum stress at a point in a machine member

The maximum shear stress due to vertical load is $$\tau_{max} = \frac{VQ_{max}}{I_c b}=\frac{4V}{3A}=\frac{4*3kN}{3\pi25^2}$$ And ot happens at the horizintal axis passing through the centroid. The ...
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1 vote

Find the maximum stress at a point in a machine member

You are not alone, many people are confused about the moment of inertia and polar moment of inertia of the circular shape, $I, I_p$, and their uses. Let's review two equations: $\sigma_b = \dfrac {My}{...
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1 vote
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Find the maximum stress at a point in a machine member

Assuming x is the horizontal axis parallel to P =15kN (+x to the right, -x to the left) y is the vertical axis on the plane (+y upwards, -y downwards) z is the axis perpendicular to the x-y (coming ...
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1 vote

BMD of the beam joined at intersection

There is no error in your diagram. if this is the moment diagram the short beam moment diagram should be a superposition of a triangle due the concentrated load from the long beam and the parabola ...
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1 vote

BMD of the beam joined at intersection

With the selection of constraints you have selected it is as if the longer beam (C and D) is resting (or is being supported by) the shorter beam (A and B). What happens is that while the load is ...
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1 vote

Can Sheet Metal Be Formed With Bends At Weld Joints?

Depends on base metal, filler metal ( if any ) and weld process and technique. Welds may be weaker or stronger ; more or less ductile than the base metal. No problem with a properly made weld in the ...
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formula for M(x) - Shear Force and Bending Moment Diagrams

Let's clear the question first: The shear and moment diagrams indicate this is a cantilever beam supported at the left end, and the system is in equilibrium under the applied loads (in green) and the ...
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1 vote

Maximum Shear force in diagram

TL;DR: If your goal is to find likely points of failure, take the absolute value It may seem I'm repeating what other have said. I'm merely trying to expand and I'll be trying to give another angle on ...
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