Determine the reaction force at the hinge Determine the reaction force at the hinge

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Remembering that a moment can NOT be supported at the hinge C: A statically indeterminate structure is a structure that has more unknown reactions that can be discovered using the equations of statics summing forces and moments.

However, it gets ridiculously tedious for many degrees of indeterminacy.

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To find the reactions, we place a statically equivalent load in the middle and sum glee season 1 sectionals online dating forces and moments about on of the support locations and calculate Ra and Rb. Draw each beams shear and moment diagram accordingly to attain the transferred moments and shears.

Deflections of Statically determinate structures There are a ton of ways to calculate deflections for determinate structures.

Feel free to email me any questions. Here is are the two governing equations and the procedure for analyzing any structure not that theta A and theta B are the left and right rotations, respectively: The force method, however is the basis for calculating member stiffnesses for more advanced methods of structural analysis.

How should I define the properties to get your results?

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Also, a new version of the program 3. I'll try to use more complicated loading conditions and I'll introduce hinges. SkyCiv Beam is pretty handy for analyses like this and it's a good way to check your logic, answers and working out. Force Method Lets look at the first and easiest method, the Force Method.

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So, I'll go into depth with my analysis of shear and moment diagrams. Matrix Analysis Matrix analysis is as far as you can take traditional Structural Analysis, that is, to analyze each member individually and compute all the internal, external, or end forced. Once all the elemental stiffnesses have been assembled they are then transformed to the global coordinate system and compiled into the structure stiffness matrix.

Isostatic structures do not care about such things. The structure stiffness matrix may also be condensed for instance, neglect axial deformations or partitioned as the user requests. Here are all the basics: Here is another example, except there is a cantilevered end at the end of the simple support and a concentrated moment.

Now, to find the FEM for a member, just look at the following equations and plug in the same values give to you in a problem: In the indeterminate case, we must use the member properties E, I, L to find reactions.

$$\sum F_y = 0\\ 11 - 6 - 2 + H_C = 0\\ \therefore H_C = 3\text{ kN}$$

Another example worked out in metric with the addition of a hinge. Who cares what it looks like. First I'll show you an example: Any beam has a stiffness based off its length, moment of inertia, and modulus of elasticity. A frame is a structure that has ridigidly connected members that allow for moments to be transferred.

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Lets start with a simply supported beam: That's the reason I tried to define generic properties to the materials even for such isostatic structure. So, what are the building blocks for Matrix Structural analysis?

The above example is a beam in which we know all the intermediate span end forces. This is why we have other methods.

Don't be frightened by a frame, it behaves much like a beam, in that, it is a series of beams. Lets take a look at a highly indeterminate beam: Basically, the force method is determine an unknown reaction by calculating the force that would be necessary to bring a displacement back to equilibrium.

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OK, that was horrible. For my last Shear and Moment diagram example, I'll look at a frame. So, after you have analyzed all the forces using some Structural Analysis Method, all you have to do is be a good bookkeeper to draw the shear and moment diagrams.