Some structural engineering problems that I need the solution

The cracking moment is typically only used for serviceability concerns (i.e., deflections). When estimating deflections of concrete beams, the moment of inertia will change depending on whether the beam is cracked or uncracked. I have another video on that topic: kzfaq.info/get/bejne/oK9mqtqbx9-dfac.html

Yep, zero means determinate (unless there is some other issue that causes instability).

Sorry, I wasn’t clear in the video. We did a wet cure (with burlap) for 7 days. We tested roughly one month after casting. That said, there are many applications in the real world where concrete is loaded well before 28 days, and concrete will continue to gain strength even after 28 days. It’s more accurate to say that 28 days is the laboratory standard.

Yes, the reactions are unknown. For an indeterminate structure, equilibrium alone is not enough to solve for the reactions, so that's why we need the force method (or other techniques for indeterminate structural analysis).

"r" is the number of releases, where a release counts as a single known internal force. So for example, a hinge in a beam forces the bending moment to be zero at that location - that counts as one release, because we know that M = 0 at that point. You can also have releases for shear and axial forces as well. These can even be combined. For example, a roller-like expansion joint in a bridge might count as two releases if both the axial force N = 0 and the bending moment M = 0 at that location.

@@StructuresProfH thank you!

The full answer might be a full video, but in the meantime, I'd probably take slices of the free body diagram at some angle theta (sort of like polar coordinates) rather than at some position x. For a semi-circular frame, the axial force will be tangential, the shear force will be radial, and the bending moment will still just be a moment. Even for a concentrated force at the peak of frame, the axial and shear force values will not be constants - they will vary by the angle theta. From there, you can apply equilibrium (sum of forces and sum of moments) to find the internal forces.

No, the "Cable" option will not automatically prestress the structure, though you can do that with a little work. If you have a linear mesh, Cable creates the LINK180 element designation, which is the same as you would use for a simple truss. If you have a quadratic mesh, Cable creates the CABLE280 element. This element requires tensile stress to provide adequate transverse stiffness, and may be unstable under compression - it works essentially like a hanging string or cable. For most applications, either Link/Truss or Cable would work for applying prestressing, but I think Link/Truss is a bit easier to deal with. Either way, to apply prestressing you need to define an initial stress in the link or cable. The INISTATE command using Mechanical APDL is the way to go.

@@StructuresProfH Thanks Dear Professor Could you create such a 3D video on KZfaq? What material do I need to define for the cables? I must set Link/Truss option?

That is correct!

Yes, the Ax and Cx reactions are the thrust forces. Normally these could be resisted by a ceiling or rafter tie. A collar tie near the peak of roof does not effectively reduce these thrust forces. I believe the primary purpose for collar ties is to better secure the rafters to the ridge beam. Anyway, if you don't have a ceiling tie, that thrust force needs to be resisted by the walls that support the roof. The other option is to have a structural ridge beam. In structural analysis terms, that means adding a third vertical support at the roof peak - this effectively eliminates the horizontal thrust forces because the truss is no longer being "squashed" out by the vertical load.

Yes, the moment diagram sign is relevant if some is negative and some is positive. The sign gives you the direction of curvature (positive opens up or "smiles" while negative opens down or "frowns"). It is important to keep this consistent in general when taking the moment of the area. That said, if the sign is all positive or all negative, I usually handle the signs intuitively (some might say lazily!) for the moment area method just by considering the deflected shape geometry. The negative sign in the second example is reflected by the fact that the deflected shape is below the tangent, whereas the positive sign in the first example is reflected by the fact that the deflected shape is above the tangent.

@@StructuresProfH Awesome, did some examples and its making much more sense.

Happy to help!

The hinge certainly doesn't help, but you will still get horizontal (X-component) reactions even without the hinge. As the load presses down on the structure, it tends to "flatten out" which will be resisted as horizontal reactions. The hinge means it tends to "flatten" more under vertical load than an equivalent system without a hinge, but the phenomena is present for either case.

Why is it then with truss analysis vertical loads never transfer lateral force to the roller/pin? Due to a 3 force member in equilibrium? And in the roof case, the bottom chord would resist the tension?

@@WG-ft6tz For truss analysis, we typically assume that one support is a pin and the other is a roller (meaning, it allows for horizontal movement). In this configuration, any horizontal force is resisted by tension in the bottom chord. However, if both supports are pins (meaning both resist horizontal motion), then you will once again get horizontal reactions even if you have a bottom chord. This is because the deformation of the truss will push these two supports outward, which is resisted by inward horizontal reactions.

Ah thank you! So used to analyzing pin/roller trusses in examples. Subscribed!