Concrete Beams Moment Capacity

The MasterSeries Concrete design calculates the Moment Capacity for the provided reinforcement and not a perfectly balanced section as per 3.4.4.4.  Clause 3.4.4.4 will be used for the sizing of reinforcement during auto sizing and then the Moment Capacity calculated for the provided reinforcement. 

Fundamental to this process is whether compression reinforcement should be considered.  In the basic data & defaults table, in the “Design & Grades” tab, you can set when you want to consider compression reinforcement by adjusting the k’ limit.  If K (=M/bd2fcu) is above this limit then compression reinforcement will be considered.  Using compression steel will mean that your link longitudinal spacing is limited to 12 x (Smallest Compression Steel Diameter).

K’ limit = 0.000 = always try to use compression steel

K’ limit = 0.156 = Only use compression steel once you reach the singly reinforced limit

K’ limit = 9.999 = Never use compression steel

Compression steel may not actually be used.  The program will only use compression steel if it has compressive strain eg:

If X is less than d’ then there is no compression reinforcement. 

If X is close to d’ then there is compression reinforcement but because the strain is small then the stress and thus its effect is small.

Reference: Kong & Evans: Reinforced and Prestressed Concrete, 3rd Edition. Fig 4.4-3  

The Moment Capacity of the section is determined by positioning the neutral axis so that Fc = Ft

Allowing for any code restrictions.

Note Fy and Fy' are dependant of the degree of strain in relation to the concrete 0.0035 strain.

Limiting X/D to 0.5 implies Fy always reaches yield at 460 N/mm2

ε’=0.0035 (X-d’)/X           

Fy’= ε’ E  but <= Fy (full yield) = 460 N/mm2 (for high yield bars to BS8110)

Ft =0.95 As fy

Fcconc = K1 Fcu (B X) 

Fcsteel = 0.95 As' fy'

Fc= Fcconc  + Fcsteel

This gives us a value of X (limited by the code)

Thus taking moments about "As" gives

z = (d - k2 X)

Mc = Fcconc z +  Fcsteel (d-d')