4

Modern building failure due to tipping is rare but did occur, usually under strong earthquakes and loss of foundation (soil and structure), as the tilt will shift the gravity center of the building that induce a tremendous amount of stress on the foundation piling and the soil mass surrounding the piling. So, how much is too much for a building to handle (...


3

The hinged region at B is not a support, actually. Thats just a connection (or to be more precise, a pinned connection). A pinned support is something different; a pinned support is something what you see on the right end C. The support itself is connected to the ground (for example), and cannot translate in any of the directions (which means that the right ...


2

Like you said at point B there will be a reaction force from the left. However, if you look that system in isolation, that reaction needs to be supported at the end. And that force at B creates a reaction moment on B. Since the reaction at B will be equal to P/2 (just take the FBD of the right part and calculate the reactions), then the bending moment at ...


2

An internal hinge is a special device used to link two beam segments. Similar to the typical pin support, it can generate reactions in the direction opposite to the load (applied force), with the condition that structural equilibrium must be maintained within the support, $\sum F_x = 0$ and $\sum F_y = 0$. Both the systems above are considered as "...


2

One way to imagine the force on the beam AB is to substitute the BC with just its tributary load P/2, (the support it gets from the hinge). Now we have only a cantilever beam AB with a concentrated load of $\ \frac{P}{2} $ applied at the left hand. So the reaction moment is as the book says: $\ M=\frac{P}{2}*L=\frac{PL}{2}$


1

It depends what you think should be the frequency of the external force, which will cause it to vibration. If the frequency of the external force is overlapping with any of the natural frequencies, then the structure resonates and you have high amplitude of vibration, which can catastrophically damage the structure.


1

Assuming that the model is adequate and appropriate, then to answer your second question: Which frequency out of those five is right? All of those modes and frequencies are possible in the structure. Usually the frequencies are provided in increasing order (i.e. the numerical smallest is presented first etc). The frequency that is usually more important, ...


1

You need to know what type of lumber is used in your ceiling to know its strength for moment and shear,$F_b \ , V_{allowable}$ and its elastic modulus, E. but for illustration assume a lower range of $$F_b=1000psi \ and\ V=100psi$$ Then your moment is $$M=\omega l^2/8= \omega*(11*12)^2/8=2178\omega$$ you beam elastic module $S_x$ is $$S_x=bh^2/6=2*8.8^2/6=...


1

Poisson's ratio is defined in the case of uniaxial tensile testing. As such the x axis is in the direction of the loading, while the y and z axis are transverse. In isotropic materials it doesn't make any difference which axis the material is tested. However for anisotropic (i.e material that don't behave in the same way in all directions), there are ...


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