Theory and design of Structures

Function of longitudinal stiffner( seldom used). @theoryanddesignofstructures

Functions of transverse stiffners. @theoryanddesignofstructures

Longitudinal and transverse stiffners. @theoryanddesignofstructures

What are stiffners( steel Structures) Stiffners are secondary plates or elements which are attached to beam Web or flange to help prevent OUT OF PLANE DEFORMATION( I.E LOCAL BUCKLING). Stiffners also serve to connect secondary beams to the main beam. We have two types of stiffners based on how they are attached to the web of the beam, transverse and longitudinal stiffners. @theoryanddesignofstructures

Continued.... the section would now undergo a different mode of failure. Considering the unbraced length of the member, we have three types of lateral torsional buckling modes: 1. When the unbraced length of the beam is less than the limit of plastic region length(Lp) then LTB will not occur. And the section would attain its plastic capacity. This Is for stocky beams. 2. When the beam length is between the limit of the plastic region(Lp) and the limit of inelastic buckling region, the section would buckle before it attains its plastic capacity, but it would pass the elastic range. Meaning irreversible type of buckling or plastic buckling would occur. 3. When the member length is less than Lr, then the section would fail before attaining even its elastic capacity. This is elastic buckling and is reversible.

LTB( lateral torsional buckling) isn't caused by APPLIED torsional moment as the name might mislead. This phenomenon is caused by the common problem associated with compression members, buckling. The cause of LTB is the compression flange of an I section trying to buckling In the plane of bending. But since the web of the section tries to resist that buckling in its weak axis together with the stabilizing effect of the tension flange and web, the whole section would undergo lateral linear and also rotational displacements, hence lateral torsional buckling. In the picture above notice how the compression flange of the I beam is displaced farther away from the vertical plane and the whole section is rotated. This is what we call LTB. LTB is geometric instability. It causes the section to fail in buckling mode before it attains its yeild strengh. One way to prevent the sections from undergoing LTB is providing appropriate lateral bracing. The bracings would cause the buckling length to decrease.

Why do steel beams have the tendency to undergo lateral torsional buckling and why is this phenomenon on a news that was 4 years ago 🤔

May 15,2015 Edmonton, Canada ...Four of seven 40-tonne steel girders remain bent over Groat Road after a phenomenon Noguez(professor at the university of Alberta, canada) referred to as lateral torsional buckling. He said it’s a "widely known and understood phenomenon" but not one that is expected to happen and he’s using the incident as an example to first-year engineering students of what not to expect from a structure.

Class 4 sections are treated as class 3 sections, but to allow for the loss of strength due to local buckling the section is reduced to "effective area".

It would benefit our economic perspective if we can use the steel section till it's full plastic capacity and it would be an advantage if the section can handle larger amounts of rotation( which would be helpful in moment redistribution in redundant systems). But that is not the case. Based on the sections stiffness towards local buckling, steel sections are classified into 4 classes, clas 1 to 4. Class 1 sections(also called plastic sections) achieve plastic capacity and redistribution is also a possibility. Class 2 sections( also called compact sections) can achieve plastic capacity yet redistribution isn't a possibility. Class 3 sections can only get to first yeild, before they achieving their plasti capacity local buckling failure will occur. Class 4 sections cannot even get to first yeild point. Local buckling will occur before the section gets to it's first yeild point.

Why do we classify steel sections into four classes? The simplest answer to this question is, because we have to be as economical as we can! Steel as a building material has a very high strength when compared with most materials used in building construction. When a material has higher strength it quiet obvious to see that it would require lesser area or thickness to fulfill most design criteria. Requiring lesser area or thickness might seem at first glance something that doesn't need any further investigation, yet it does and it is very critical. The issue with thinner section is a phenomenon called "local buckling". Think of an I section. It is composed of web and flange. And when load is applied to this section, the web or the flange can buckle before the whole section can reach to it's elastic or plastic capacity. This component buckling would render some part of the section to be ineffective and even worse the full capacity of the section cannot be utilized.

What if we intentionally remove the soil to a certain depth so that the pressure that the new structure is coming with is smaller than the overburden? If one applies this principle, the types of foundation that is going to be achieved is called floating( also called buoyancy foundation) , since the building is basically floating like a boat on water. The disadvantage of such foundations is that, sometimes the excavation depth required is very large and considering basement floor would be inevitable to use the space created below ground floor. And sometimes basement wouldn't be included and the resulting foundation system would be "cellular raft" which is shown in the picture above.

When the bearing capacity of a given soil is very low, it is very common to go deeper to find a better bearing strata. But sometimes the required excavation depth is so intense, the way we understand the situation changes, especially if it is clay and consolidation settlement Is in the picture. We have two types of clay soil in relation with the effective overburden pressure( the pressure that the soil is experiencing at the time of consideration and it is effective 😊). We have normally consolidated clay which is simply a soil that has never carried the load that is being applied to it, meaning it is going to experience a larger settlement. On the other hand over consolidated clay is the kind that, in it's loading history, has experienced a load that is greater than the one being applied now. This type of soil undergo lesser settlement. With that said, since the overburden pressure is usually the weight of the soil above the strata being considered....

The structural or geothechnical engineers out there, do u check the stress overlap between your closely spaced footings or u just go " as far as it is isolated and isn't overlapping"?

.....if the summation of stress between the two footings is greater than the allowable, then combined footings become inevitable.

Why do we have to place footings at least "B" distance from each other? Let me rephrase, isolated footings designed independently have to be placed in such a way that an adequate gap is ensured. That adequate gap is "B", which Is the larger size width of the two footings under consideration. Following boussinesq stress distribution under a point load one can see that the stress from one footing extends B/2 distance from the face of the footing. Meaning if two footings with B width are placed in such way that the clear distance from the two is less than B, then the stress at B/2 from the footings is the sum of stress from the two. Can we place footings such that the clear spacing between the two is less than B? Or do we have to go for combined footings? The answer to this question Is to verify that the summation of the stress from the two is less than the allowable bearing capacity of the soil. If indeed the summation of stress from the two is less than the allowable no need to go for combined footings.

while designing T/L beams the location of the neutral axis plays a vital role. Since the neutral axis can be in the flange or in the web, we must first exactly locate where it is. Once the location of the neutral axis is determined either of the two cases would be followed to design the beam, 1) neutral axis within the flange(xuDf). This leads to a more demanding analysis to determine the effect of the flange and web in compression.

T/L beam effect, for drop beams (beam whose top is in similar elevation with the slab top), is observed for hogging or positive moment regions. Since concrete is effective in carrying only compression, it is convenient to state for a uniformly loaded simply supported beam that mid-span regions can be designed by taking into consideration the T/L beam effect. On the other hand, sagging or negative moment regions would lead to the development of tensile stress in the flange, which would automatically render the concrete useless since concrete can’t carry tension.

Monolithically casted RCC beam and slab have the tendency to create T/L beam effect even if the beams are intended to be rectangular once. The portion of the slab close to the beam would try to share part of the compressive longitudinal stress developed along the beam. T/L beam is simply the result of the location of the beam. Internal beams develop T beam effect while edge beams develop inverted L beam effect. Both beam types follow almost similar design principle, they only differ in the portion of slab to be considered as part of the slab.

Beam on elastic foundation is the best way for foundation design! you model the soil using Area spring/spring properties and the software will capture the interaction between the foundation element and the soil. This approach will give you a better understanding and design moment or shear specially for mat foundations. I have some tips: Tip 1: In the absence of plate load test result you can use an approximate method to determine the soil subgrade reaction. Bowels has proposed the following equation, Ks=40*SF*σall (SF-safety factor, σall allowable bearing capacity). Tip 2: don’t reinforce your mat or footings with the maximum moment around columns. Since the design moment is located at the face of column, at least try to read the moment at the face of column. Otherwise you would reinforce your mat for peak moment and end up being uneconomical. Tip 3: don’t forget to model the lateral passive earth pressure preventing your footing from sliding. Otherwise your model would be unstable. Tip 4: If you are using SAFE, you can model the soil with “soil property” and you can draw strips to help you read moment easily and perform a better design (since strips include torsional moment in calculating design moment, it makes your work easy. If you use finite element method to design your footing elements, don’t forget to use WOOD and ARMER method to allow torsional moments in your design.