Detailed Example: Left Support Steel Hogging

Cover = 55 mm

Fcu = 40 N/mm2

Fy = 460 N/mm2

Note in the following calculations the conversion to known units are carried out internally (eg N to kN).

K1= 0.45(1-√ Fcu/52.5)   =  0.396

K2=  [(2- √ Fcu/17.5)2 + 2] /    [4 (3-√ Fcu/17.5) ]  = 0.444

d’= 55 + 12 + 32/2 =83 mm

d= 1000 – 55 -12 – (15 20 + 12 100)/27 = 877.444 mm

Assume X from computer iterations

X = 309.77 mm

As=27 40 40/4 pi =33,929 mm2  

As’=15 32 32/4 pi =12,063.7 mm2  

ε’=0.0035 (309.77-83)/309.77           =           2.5622 E-3

Fy’= ε’ 200 = 512 > 460 full yield           =       460 N/mm2

εs=0.0035  (877.4-309.8)/309.8           =           6.414 E-3

Fy= εs 200 = 1282 > 460 full yield=       460 N/mm2

Fcsteel = 460 0.95 12,063.7           =    5,271.836 kN

Fc conc=.396 40 2000 309.77          =    9,813.513 kN

Fc = Fcsteel + Fcconc                                    =  15,085.349 kN

Ft = 33929 460 0.95                        =  14,844,453 kN

δ                                                  =       240.896 kN

δ=240.896/14844.453 100          =           1.622 % error (acceptable for hand calc)

z= d - K2 X = 877.4-0.44 310          =     739.907 mm

Mcconc = 9,813 (877.4-0.44 310)           =  7,261.078 kNM

Mcsteel = 5,271 (877-83)                    =  4,188.178 kNM  

Mc = Mcconc + Mcsteel                    =11,449.256 kNM