# Tag Info

## Hot answers tagged statics

### Why are screw holes in most of the door hinges in zigzag orientation?

More compact configuration that fully utilizes the area of the leaf. Avoid stresses concentrated on a single plane that is likely to cause the base material to progressively fail in shear or split. ...
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### Why are screw holes in most of the door hinges in zigzag orientation?

Because the screws go into wood and if the screws are in line then the wood will most often split between the screws in the grain direction and then the screws come loose.
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### How should I position two shelf supports for the best distribution of load?

As with all good things, it depends. If you can assume that your supports are totally stiff and that the loading on the shelf will be approximately uniform, then you basically have the following ...
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### Why does a gear have extra holes?

Different gears have different drivers for having holes. One way you can categorize gears is by whether they are used primarily for transferring: motion: transferring angular position and angular ...
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### Why are screw holes in most of the door hinges in zigzag orientation?

Staggering the screws will give a better chance for some of them to penetrate into solid grain. and discourage toilet paper perforation pattern. Provide for larger torque resistance. keeping the ...
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### What is the advantage of statically indeterminate structures?

For example, take a look at the following static systems. Assume they have the same length and the same (constant) cross-section. Thus an equal allowed bending moment $M_u$. The first system is ...
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### 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 ...
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### Why does the minimum force have to be parallel to the incline?

The minimum force is in the direction the object would move without that force. Clearly the object would move along the inclined plain, down and right in your diagram. Put another way, its the ...
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### Why does a gear have extra holes?

In addition to the other answers such as weight reduction and inertia, there are other possibilities: Often there can be a precision machined hole for timing purposes. A common solution for some / ...
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### Why does the upper wing skin fail in buckling and lower wing skin does not?

In a wing the normal situation is that the aerodynamic force is upwards (resisting gravity). You are right that there is some shear and a fair amount of torsion, but the result is that: the top side ...
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### How does a church built from stones survive 70 years under water?

See the rubble around it? that's other buildings that were less robustly put together that fell apart. And you can see the first floor of another tower that did collapse. Older building techniques don'...
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### Given the tensile strength of a rod, how do you calculate the max weight that can be hung from it?

You're hanging it from a rod supported by both ends - and need to use the bending equations. For this case (case 7 in the link), the max weight is: $$W_{max} = \frac{\pi d^3 \sigma}{8L}$$ $\sigma$ ...
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### Mathematical representation of hinge and pin connection

I believe you have chosen a poor reference. Indeed, that link has absolutely nothing to do with structural analysis, but rather a specific implementation in steel structures. A ...
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### 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 ...
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### 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 ...
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### Why does a gear have extra holes?

It could be for combination of reasons. lubrication: the holes will both pump and let the lubricant pass through. Reduced angular momentum reduces backlash and adds to gearbox responsiveness. ...
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### Maximum Shear stress in Beams

You've got your terms confused. The maximum shear stress at the midpoint is equal to $$\tau_{max} = 1.5\frac{V}{A} = 1.5\overline\tau$$ where $\dfrac{V}{A}=\overline\tau$, which is the average ...
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### How much weight can an aluminum tube beam support?

We use this equation for a simply supported beam loaded at its center with 200lbs. M= P x L/4 =200 x 3 /4 = 150 lbs.ft for calculating the tube stress we convert this to 150 x 12 = 1800 lbs.inch ...
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### Why does a simple pin-ended triangular (arched/curved) beam deflect more due to secondary effects (non-linear analysis)?

Play around with a simple version of this structure, made from a sheet of paper fixed in a slight curve, and see what happens when you apply a load to the mid point. If the first example, any ...
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### Why do we ignore horizontal reactions at roller supports?

If a bar is only supported by roller supports (which allow for horizontal displacements) and a horizontal force is applied, the bar will not suffer any internal forces because the entire structure (...
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### Isn't a pin support supposed to prevent translation both horizontally and vertically?

It's simple: while B is a pinned support, C is a roller. You can see that in the figure, where B is drawn clearly bolted to the "ground" while C isn't. In fact, the contact between C and the "wall" ...
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### Does a washer really increase static friction force?

No it doesn't, and it isn't meant for that either. A standard flat washer, that is. It's meant to give the nuts and bolts a better support, and it protects the material against the nut which may ...
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### Why does a gear have extra holes?

Also someone may have to pick the machine up and carry it. Reducing weight is not just related to the intrinsic function of the machine, its shafts and so on.
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### 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 ...
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### Replacing a straight rigid link by a curved rigid link

I understand your structure is as follows (where the circular version is just an example of a "curved" link): One thing that is clear is that this structure is isostatic, therefore the external ...
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### Why is the moment of forces on a rigid body in static equilibrium must be zero about any point, even if the position of that point is not on the body

Consider a body to be in equilibrium under the action of forces $F_i$, $i=1,\ldots,n$ which act at locations $r_i$, $i=1,\ldots,n$. Equilibrium of the body implies \sum _{i=1}^n r_i \times F_i=0 \ \...
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### How can we derive the formula of the centroid?

Think about the centroid that way: If you have this curve $y(x)$ (first graphic), where its "mass" is its area $A$. The centroid $(x_s,y_s)$ is the place where you would have to put a point mass of ...
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### Car which can climb the ramp of higher inclination

The rear-driven car is able to climb higher inclination. Rational: Where is the engine and the weight has for sure an impact, but it is not related with rear or front driven car: You have rear-...
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### Height limits of brick and mortar tower?

I'll give you an example I first read in Gordon's book "The science of new materials". Assume you want to build a tower as high as possible, of constant cross-section A (the easiest shape ...
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