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Strain energy, Conservative force and Potential energy

What will be the conservative force $F$ in this case, which I will be using in this $\int_1 ^2F.ds = - (U_2 - U_1) $ equation to find the potential energy? I know you know that the force is $F=-kx$ (...
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Strain energy, Conservative force and Potential energy

In a bar the force causing the deflection $\delta$ is very similar to a spring potential energy under the force, F and displacement x: $$F=\frac{2U}{\delta }$$ $$U=(AL*\epsilon\sigma)/2=\frac{\sigma^...
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How did horizontal progressive collapse occur in 7 World Trade Center?

Bolts attaching gussets to columns failed in shear. The horizontal beams were attached to vertical columns with bolted gussets. Those bolts on the upper floors were heated by fire until they failed in ...
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Influence line question for calculating maximum bending moment

This question is to investigate the moment at an internal point due to the influence of the unit load "1". The solution is illustrated below. You shall repeat the steps to obtain the ...
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-1 votes

Best way to deploy a projector screen from the bottom?

A pull cord. Or fixed threaded rods and rotating nuts that then drive the rods up taking the screen with them. That way the rods will only be "visible" when extended, but covers can also be ...
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2 votes
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Natural Frequency of a Shear Frame

The basic unit of the natural frequency is $Hz$, $cycle/s$, or just $1/s$. Let's check the results by using "$m$" and "$mm$" as the base unit - 1. Use $m$ as the base unit: $\...
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1 vote

Why do wooden gate designs recommend a brace under compression instead of tension?

I think @r13 nailed it. FWIW... My preference for the cable version is based on the following, FWIW: It adds less weight to the gate. I like the "mechanical assist" look. And most ...
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Why do wooden gate designs recommend a brace under compression instead of tension?

The wood under compression is easier on the fasteners. Screws, nails, whatever. Think about the failure modes. How much weight or how many Newton Metres will it take each way before failing? Also it ...
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Solving an indeterminant truss with static redundancy of 2 confusion

Hint - On top of pin supported ends (one more than the equations for global equilibrium conditions), the two diagonal members in the middle panel possess one degree of redundancy. So you should ...
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Mechanism and static determinacy

The answer for b) should have a redundancy of second degree - j = 6, r = 6, b = 8, i = (b+r) - 2j = (8+6)-2*6 = 2. For c), redundancy of third degree - j = 5, r = 6, b = 7, i = (7+6) - 2*5 = 3. For ...
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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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13 votes

Why do wooden gate designs recommend a brace under compression instead of tension?

The frame and the brace in the first gate shown in your question seem to be joined together with simple butt joints, probably with nails to hold them together. Such joints are strong under compression ...
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72 votes

Why are two wires used in railway overhead equipment?

Overhead line worker here. It's about speed. To answer your question, the purpose of the catenary wire is to get the contact wire to lay flat, so it isn't catenary itself. In your second photo, there ...
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6 votes

Why are two wires used in railway overhead equipment?

Why two wires: A wire hanged at two points sags (it forms a "catenary curve"). The pantograph can only handle a certain sag before losing contact and arcing. The acceptable sag depends on ...
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3 votes
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Transforming the Area of a Hollow Square Section filled with concrete into the equivalent area of just steel

You can simply calculate "equivalent" cross-sectional stiffness values. Note that all non-zero terms of the stiffness matrix depend on one of these values: $EA$ or $EI$. These are the cross-...
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7 votes

Why do wooden gate designs recommend a brace under compression instead of tension?

Wood expands when exposed to moist conditions. For the first case, the elongation of the diagonal will be offset by the compressive stress, resulting in a smaller geometry change. For the second case, ...
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21 votes
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Why do wooden gate designs recommend a brace under compression instead of tension?

The reason is simple: the load applied on the gate is pretty trivial, and the brace (be it a 2x4 or a wire) is mostly added for rigidity. Indeed, you could put that 2x4 in tension and it would work ...
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3 votes

Why do wooden gate designs recommend a brace under compression instead of tension?

Because the wood brace works in compression and the wire brace works in tension. Just make a model and see how that wire will behave in compression. Also you would need different joints for the wood ...
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1 vote
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Symmetry to determine the support reactions of a statically indeterminate frame

The members and loads of the frame are symmetric about joint "B", but the supports are not, which is the source that causes non-conforming deflections when loaded. The sketches below depict ...
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12 votes

Why are two wires used in railway overhead equipment?

It isn't to do with current-carrying capacity; it is to maintain good contact between the current-carrying wire and the pantograph pickup on the locomotive, as it allows the contact wire to be ...
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0 votes

What is the cause of this cracking pattern in a simply supported beam?

Below is my inspection. Note the cracks between the support points - from diagonal near support and gradually turns vertical towards the midspan. Street View: The cracks in the circle forms the ...
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0 votes

Any way to approximate effect of two point loads with just one?

Yes, it is called the "equivalent load" method, which is to replace multiple loads with a single load to simplify the analysis. The essence is that both systems will yield the same reactions ...
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0 votes

Any way to approximate effect of two point loads with just one?

Yes, it is okay to replace two equal transverse loads with one combined load placed at the neutral axis of the beam. Unless the beam's transverse strength is not enough to support the individual loads ...
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2 votes

Work done by a force in a deformable body

Work is a strange but useful mathematical concept. It is very handy because it is conservative in inertial frames. It also has an intuitive meaning most of the time, but not always. This is what gets ...
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1 vote

Work done by a force in a deformable body

Individual work done on the body by a single force equals $F*s$ as shown on the sketch to the right. The work done by multiple forces equals the vector sum of the forces ($R$) and the absolute/net ...
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1 vote

Work done by a force in a deformable body

The work of a force is by definition vector multiplication of the force by displacement. $$W =F*x$$ Let's use two examples to clarify. In a pendulum, the work done on the part of the descending of ...
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1 vote
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Direction confusion for shear and moment when sectioning a beam

This is the first step to simplify the analytical model by applying the equivalent load concept as depicted below: Another way to examine the direction of forces at where the cantilever is cut off.
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0 votes

Max bending moment estimate

The wing design is the art of designing for strength in the most efficient way to make the plane as light as possible, while not sacrificing the strength. The part of the wing that carries the bending ...
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Max bending moment estimate

The formula for bending stress of Circular rod, $\sigma = \pm \dfrac{32M}{\pi d^3}$, $d$ is rod diameter. Rectangular rod, $\sigma = \pm \dfrac{6M}{bh^2}$, $b$ is width, $h$ is height. The ...
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2 votes

Can/should you support a sagging ceiling from above?

You don't seem to have an urgent problem, as the ceiling may have stayed there for a long period of time. However, according to the modern building code for attic space without storage, the 50 mm ...
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1 vote

Can/should you support a sagging ceiling from above?

You can use 2x10s at 48" O.C. from above and use available fasteners by Simpson or other brands to hang the 2x4d from down below. it is the common way.
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Degree of Kinematic Indeterminacy

The structure is statically indeterminate to the third degree (1+2+3 = 6 unknowns - 3 equations). The degree of kinematic indeterminacy equals the number of freedom of the joints. For your case, use ...
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0 votes

Is it valid to solve for the young's modulus required for a given critical load with Euler Columns?

Yes you can use the formula to solve for an acceptable modulus of elasticity (E) that prevents buckling. Like any mathematical formula that relates 4 variables, you can calculate any variable based on ...
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Calculations of Retaining Wall

I assume that this sketch is not up to scale otherwise this retaining wall would topple! One would need a longer and thicker toe possibly with a heal. Usually, we use the relation, $ \ \frac{RM}{OM}\...
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Is it valid to solve for the young's modulus required for a given critical load with Euler Columns?

As the expression suggests, Pcr is a function of (E, I, L), in other words, Pcr is can not be assumed as an arbitrary number, nor can be predetermined without knowing the parameters it is based on. So,...
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Is it valid to solve for the young's modulus required for a given critical load with Euler Columns?

No we could not. colums buckle under a random load usually les than the Euler's buckling load due to many reasons, such as manufacturing defects or material residual stress. Two columns with same ...
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