This chap ter de scribes in de tail the vari ous as pects of the con crete de sign pro ce dure that is used by SAP2000 only when the user se lects the AASHTO LRFD 1997 De -sign Code (AASHTO 1997). Vari ous no ta tions used in this chap ter are listed in Table III-1.
The de sign is based on user specified load ing com bi na tions. But the pro gram pro -vides a set of de fault load com bi na tions that should help satisfy re quire ments for the de sign of most bridge type struc tures.
SAP2000 pro vides op tions to de sign or check mo ment re sist ing frames of Zones 1 (low seis mic ac tiv ity), 2, 3, and 4 (high seis mic ac tiv ity) as re quired for seis mic de -sign pro vi sions. The de tails of the de -sign cri te ria used for the dif fer ent seis mic zones are de scribed in the fol low ing sec tions.
Eng lish as well as SI and MKS met ric units can be used for in put. The code is based on Inch- Kip- Second units. For sim plic ity, all equa tions and de scrip tions pre sented in this chap ter cor re spond to Inch- Kip- Second units un less oth er wise noted.
Acv Area of con crete used to de ter mine shear stress, sq- in Ag Gross area of con crete, sq- in
As Area of ten sion re in force ment, sq- in As¢ Area of compression re in force ment, sq- in
As required( ) Area of steel re quired for ten sion re in force ment, sq- in Ast To tal area of col umn lon gi tu di nal re in force ment, sq- in Av Area of shear re in force ment, sq- in
a Depth of com pres sion block, in
ab Depth of com pres sion block at bal anced condition, in amax Maxi mum al lowed depth of com pres sion block, in b Width of mem ber, in
bf Ef fec tive width of flange (T- Beam sec tion), in bw Width of web (T- Beam sec tion), in
Cm Co ef fi cient, de pend ent upon col umn cur va ture, used to cal cu late mo ment mag ni fi ca tion fac tor c Depth to neu tral axis, in
cb Depth to neu tral axis at bal anced con di tions, in
d Dis tance from com pres sion face to ten sion re in force ment, in d¢ Con crete cover to cen ter of re in forc ing, in
ds Thick ness of slab (T- Beam sec tion), in Ec Modu lus of elas tic ity of con crete, psi
Es Modu lus of elas tic ity of re in force ment, as sumed as 29,000 ksi fc¢ Speci fied com pres sive strength of con crete, ksi
fy Speci fied yield strength of flex ural re in force ment, ksi fyh Speci fied yield strength of shear re in force ment, ksi h Di men sion of col umn, in
Ig Mo ment of in er tia of gross con crete sec tion about cen troi dal axis, ne glect ing re in force ment, in4
Ise Mo ment of in er tia of re in force ment about cen troi dal axis of mem ber cross sec tion, in4
k Ef fec tive length factor L Clear un sup ported length, in
Table III-1
List of Symbols Used in the AASHTO code
M1 Smaller fac tored end mo ment in a col umn, kip-in M2 Larger fac tored end mo ment in a col umn, kip-in Mc Factored mo ment to be used in design, kip-in
Mb Non sway com po nent of fac tored end mo ment, kip-in Ms Sway com po nent of fac tored end mo ment, kip-in Mu Fac tored mo ment at sec tion, kip-in
Mux Fac tored mo ment at sec tion about X-axis, kip-in Muy Fac tored mo ment at sec tion about Y-axis, kip-in Pb Ax ial load ca pac ity at bal anced strain con di tions, kip Pe Euler buck ling strength of col umn, kip
Pmax Maxi mum ax ial load strength al lowed, kip P0 Ax ial load ca pac ity at zero ec cen tric ity, kip Pu Fac tored ax ial load at sec tion, kip
r Ra dius of gy ra tion of col umn sec tion, in Vc Shear re sisted by con crete, kip
VD+L Shear force from span load ing, kip Vu Fac tored shear force at a sec tion, kip
Vp Shear force com puted from prob able mo ment ca pac ity, kip a Re in forc ing steel over strength fac tor
b is a fac tor in di cat ing the abil ity of di ag o nally cracked con crete to trans mit ten sion
b1 Fac tor for ob tain ing depth of com pres sion block in con crete bd Ab so lute value of ra tio of maxi mum fac tored ax ial dead load to
max i mum fac tored ax ial to tal load
q An an gle of in cli na tion of di ag o nal com pres sive stresses with the lon gi tu di nal axis of beam or column
ds Mo ment mag ni fi ca tion fac tor for sway mo ments
db Mo ment mag ni fi ca tion fac tor for nonsway (braced) mo ments ec Strain in con crete
es Strain in re in forc ing steel j Strength re duc tion fac tor
Table III-1
List of Symbols Used in the AASHTO code (continued)