The SRSS rule is also relatively simple as the Square Root of the Sum of Squares rule corresponds to a “white noise” behavior. As the different modes are completely uncorrelated the modes are superimposed in a Pythagorean manner and the standard formula for getting the max/min total response values is:

R_tot,max = √ (ΣR_i², for i=1 to n)

R_tot,min = -√ (ΣR_i², for i=1 to n)

For concomitant values, we have a similar to the ABS rule, with sgn(Σ) denoting the sign of (Σ(Rk,i²*sgn(Rl,i)).

Rtot,con = sgn(Σ)*√(ΣΣ(Rk,i²*sgn(Rl,i))) for values concomitant with max values, and;

Rtot,con = - sgn(Σ)*√(ΣΣ(Rk,i²*sgn(Rl,i))) for values concomitant with min values

In matrix form, we can write this in the same form as given in the textbooks for DSC and CQC rules, with the correlation matrix being the unit matrix (ρij=1.0 for i=j, ρij=0.0 for i≠j):

Rtot,max = √([R]T*[ρ]*[R])

Brought down to the component level and introducing sign adjustment we get the maximum/minimum values, with sgn(Rk,i) and sgn(Rk,j) denoting the sign of the respective value.

Rk,tot,max = √( ΣΣ(Rk,i*sgn(Rk,i)*ρij*Rk,j*sgn(Rk,j)) ) 

Rk,tot,min = - √( ΣΣ(Rk,i*sgn(Rk,i)*ρij*Rk,j*sgn(Rk,j)) )

For concomitant values, there is the only difference that we have to use the sign of the leading value for sign adjustment, rather than using the sign of the actual component. Denoting l as the leading component we get for concomitant values, with sgn(Σ) denoting the sign of (ΣΣ(Rk,i*sgn(Rl,i)*ρij*Rk,j*sgn(Rl,j)).

Rk,tot,con = sgn(Σ)*√( |ΣΣ (Rk,i*sgn(Rl,i)*ρij*Rk,j*sgn(Rl,j))| ) 

Rk,tot,con = - sgn(Σ)*√( |ΣΣ (Rk,i*sgn(Rl,i)*ρij*Rk,j*sgn(Rl,j))| )