apply Ld/db = 3/40 (rad f'c/fy) * (Alpha*beta*gamma*lamda) / ([C + Ktr]/db)
Check ACI 318-08 Eq 12-1. It was developed by some smart south African dude.
Enjoy.
Ld={(3*fy*Ѱt*Ѱe*Ѱs)/(40*λ*(f'c)^.5*[(cb+Ktr)/db)])}*db
Ktr = (40*Atr)/sn read ACI -Ψ reinforcement factors related to coatings, size & position
however an easy check for cases where f'c = 4000 ; Gr 60 steel
Lb = 47db
(these are cases with min cover, min clear spacing, min clear cover, min ties & stirrups)
if less coverage and closer spacing
Lb = 71db
caveat - Structural engineers are paid to perform this design.....use 'em
When the maximum stresses in steel and concrete simultaniously reaches allowable value the section is called balanced section when the %of steel in a section is less than that required for a balanced section it is under reinforced section when the %of steel in a section is more than that required for a balanced section it is over reinforced sectionover reinforcement is as per section design I.e Ast1+Ast2>Ast Ast1+Ast2
There are two basic reasons 1. In over reinforced section failure happens due to concrete which is sudden without any type of warning like bending or deflection.... 2. Steel is one of the most costly material used in construction work so from the economical view it is also undesirable to provide over reinforced section...
the purpose of strength reduction factor is used to take into account the uncertainties of material strength, inaccuracies in the design equations, approximations in analysis, possible variations in dimension's of the concrete section and placement of reinforced, the importance of member of structure of which they are part, an so on. Column is designed stronger than beam it means during strong earthquake column member remain elastic so it can provide stability and strength of the stories above.
It is economical. Full cross-section of member is utilized. Increases durability. Reduces corrosion of steel. Increase in shear capacity. Larger spans can be constructed. It allows rapid construction.
section modulus of any section is the ratio of the moment of inertia to the distance of extreem fibre from the neutral axis. plastic section modulus is the section modulus when the cross section is subjected to loading such that the whole section is under yield load. numerically it is equal to the pdoduct of the half the cross section area and the distance of center of gravity of tension and compression area from neutral axis
Reinforced concrete is made by placing steel bars in the tension zone of the beam x-section.
When the maximum stresses in steel and concrete simultaniously reaches allowable value the section is called balanced section when the %of steel in a section is less than that required for a balanced section it is under reinforced section when the %of steel in a section is more than that required for a balanced section it is over reinforced sectionover reinforcement is as per section design I.e Ast1+Ast2>Ast Ast1+Ast2
Under Reinforced Section
There are two basic reasons 1. In over reinforced section failure happens due to concrete which is sudden without any type of warning like bending or deflection.... 2. Steel is one of the most costly material used in construction work so from the economical view it is also undesirable to provide over reinforced section...
when section of the beam is restricted and the moment due to incoming load is not resisted by moment due to concrete then we have to provide reinforcement in compression zone also to take this extra incoming load
V. K. Yudin has written: 'Behavior of reinforced concrete beams with rectangular cross-section subjected to combined torsion and flexure'
A section which has twice as much as the usual amount of reinforcement.
Singly reinforced beams have reinforcing only on the tension face. Doubly reinforced beams have reinforcing on the tension and compression face. Doubly reinforced beams can increase section capacity, but are primarily used to increase the ductility of the concrete beam. In certain codes, if the concrete section is controlled by the concrete failing in compression before the tension steel rebar yields (called a compression-controlled or brittle section), the calculated section capacity must be reduced to account for the brittle and sudden/unpredictable nature of a compression controlled (also called a brittle) failure. In order to make the section controlled by the yielding of the tension reinforcement (called a tension-controlled or ductile section), the ductility must be increased. This can be accomplished by adding steel in the compression zone, which gives strength to the compression area, thereby delaying the failure of the concrete. Enough compression steel can cause the section to switch from a brittle mode-of-failure to a ductile mode-of-failure, thereby permitting the designer to not decrease the section capacity from its calculated value. When identifying a doubly- reinforced beam, be sure that the steel in the compression area is meant to be for strength. Oftentimes, all faces of a beam will have some reinforcing for temperature/shrinkage protection and to tie the stirrups to. Steel that is only there for temp/shrinkage or to facilitate tying the rebar will usually be small and not much of it. In buildings, they will be often #3 bars @ 12" centers. In bridges, they may be #4 bars. These small bars should not be counted as compression-zone reinforcing. Look for bars in the compression zone that are of similar size to the main tension reinforcing.
A singly reinforced beam only has steel reinforcement on the tension side (along the bottom of the cross section) where as a doubly reinforced beam has steel reinforcement on both the tension and compression sides, ie. the top and bottom of the cross section.
From ACI 318; 1) Solve for a (whitney compressive stress block) 2) Determine moment from force couple
What is the unit weight of aluminium section and how its calculate
It is a column having composite reinforcement having MS bar at the middle of the section either T, I ,O or rectangular shapes and HYSD bars at the corners. A composite column is one in which a structural steel shape like I,O are encased in reinforced concrete..