Transformation factors
Ingeania uses the following transformation factors in its Single Degree of Freedom calculator SDOF for the analysis of structural elements subjected to dynamic loading.
| Load and Mass Distribution | Resistance Domain | Load Factor | Mass Factor | Load Mass Factor | Maximum Resistance | Linear Stiffness | Equiv. Linear Stiffness | Dynamic Reaction |
| Kl | Km | Klm | Rmax | kl | ke | V | ||
 |
Elastic | 0.64 | 0.50 | 0.78 | 8Mp/L | 384EI/(5L3) | 0.39R+0.11F | |
| Plastic Bending | 0.50 | 0.33 | 0.66 | 8Mp/L | 0 | 0.38R+0.12F | ||
| Plastic Membrane | 0.50 | 0.33 | 0.66 | 4Np/L | 2Npymax/L | |||
 |
Elastic | 0.64 | 1.00 | 1.56 | 8Mp/L | 384EI/(5L3) | 0.50R | |
| Plastic Bending | 0.50 | 1.00 | 2.00 | 8Mp/L | 0 | 0.50R | ||
| Plastic Membrane | 0.50 | 1.00 | 2.00 | 4Np/L | 2Npymax/L | |||
 |
Elastic | 1.0 | 0.49 | 0.49 | 4Mp/L | 48EI/(L3) | 0.78R-0.28F | |
| Plastic Bending | 1.0 | 0.33 | 0.33 | 4Mp/L | 0 | 0.75R-0.25F | ||
| Plastic Membrane | 1.0 | 0.33 | 0.33 | 4Np/L | 2Npymax/L | |||
 |
Elastic | 1.0 | 1.0 | 1.0 | 4Mp/L | 48EI/(L3) | 0.78R-0.28F | |
| Plastic Bending | 1.0 | 1.0 | 1.0 | 4Mp/L | 0 | 0.75R-0.25F | ||
| Plastic Membrane | 1.0 | 1.0 | 1.0 | 4Np/L | 2Npymax/L | |||
 |
Elastic | 0.87 | 0.52 | 0.60 | 6Mp/L | 56.4EI/(L3) | 0.525R-0.025F | |
| Plastic Bending | 1.0 | 0.56 | 0.56 | 6Mp/L | 0 | 0.52R-0.02F | ||
| Plastic Membrane | 1.0 | 0.56 | 0.56 | 6Np/L | 3Npymax/L | |||
 |
Elastic | 0.87 | 0.76 | 0.87 | 6Mp/L | 56.4EI/(L3) | 0.525R-0.025F | |
| Plastic Bending | 1.0 | 1.0 | 1.0 | 6Mp/L | 0 | 0.52R-0.02F | ||
| Plastic Membrane | 1.0 | 1.0 | 1.0 | 6Np/L | 3Npymax/L | |||
| Load and Mass Distribution | Domain | Kl | Km | Klm | Rmax | kl | ke | V |
 |
Elastic | 0.53 | 0.41 | 0.77 | 12Mps/L | 384EI/(L3) | 307m1m1=EI/(L3)*(1.5Mps/(Mps+2Mpm)+0.25) | 0.36R+0.14F |
| Elasto-Plastic Bending | 0.64 | 0.50 | 0.78 | 8(Mps+Mpm)/L | 384EI/(5L3) | 0.39R+0.11F | ||
| Plastic Bending | 0.50 | 0.33 | 0.66 | 8(Mps+Mpm)/L | 0 | 0.38R+0.12F | ||
| Plastic Membrane | 0.50 | 0.33 | 0.66 | 4Np/L | 2Npymax/L | |||
 |
Elastic | 0.53 | 1.00 | 1.88 | 12Mps/L | 384EI/(L3) | 307m1m1=EI/(L3)*(1.5Mps/(Mps+2Mpm)+0.25) | 0.50R |
| Elasto-Plastic Bending | 0.64 | 1.00 | 1.56 | 8(Mps+Mpm)/L | 384EI/(5L3) | 0.50R | ||
| Plastic Bending | 0.50 | 1.00 | 2.00 | 8(Mps+Mpm)/L | 0 | 0.50R | ||
| Plastic Membrane | 0.50 | 1.00 | 2.00 | 4Np/L | 2Npymax/L | |||
 |
Elastic | 1.00 | 0.37 | 0.37 | 4(Mps+Mpm)/L | 192EI/(L3) | 0.71R-0.21F | |
| Plastic Bending | 1.00 | 0.33 | 0.33 | 4(Mps+Mpm)/L | 0 | 0.75R-0.25F | ||
| Plastic Membrane | 1.00 | 0.33 | 0.33 | 4Np/L | 2Npymax/L | |||
 |
Elastic | 1.00 | 1.00 | 1.00 | 4(Mps+Mpm)/L | 192EI/(L3) | 0.71R-0.21F | |
| Plastic Bending | 1.00 | 1.00 | 1.00 | 4(Mps+Mpm)/L | 0 | 0.75R-0.25F | ||
| Plastic Membrane | 1.00 | 1.00 | 1.00 | 4Np/L | 2Npymax/L | |||
 |
Elastic | 0.80 | 0.41 | 0.51 | 9Mps/L | 260EI/(L3) | 212m1m1=EI/(L3)*(1.5Mps/(Mps+2Mpm)+0.25) | 0.48R+0.02F |
| Elasto-Plastic Bending | 0.87 | 0.52 | 0.60 | 6(Mps+Mpm)/L | 56.4EI/(L3) | 0.52R-0.02F | ||
| Plastic Bending | 1.00 | 0.56 | 0.56 | 6(Mps+Mpm)/L | 0 | 0.52R-0.02F | ||
| Plastic Membrane | 1.00 | 0.56 | 0.56 | 6Np/L | 3Npymax/L | |||
 |
Elastic | 0.80 | 0.64 | 0.80 | 9Mps/L | 260EI/(L3) | 212m1m1=EI/(L3)*(1.5Mps/(Mps+2Mpm)+0.25) | 0.48R+0.02F |
| Elasto-Plastic Bending | 0.87 | 0.76 | 0.87 | 6(Mps+Mpm)/L | 56.4EI/(L3) | 0.52R-0.02F | ||
| Plastic Bending | 1.00 | 1.00 | 1.00 | 6(Mps+Mpm)/L | 0 | 0.52R-0.02F | ||
| Plastic Membrane | 1.00 | 1.00 | 1.00 | 6Np/L | 3Npymax/L | |||
| Load and Mass Distribution | Domain | Kl | Km | Klm | Rmax | kl | ke | V |
 |
Elastic | 0.58 | 0.45 | 0.78 | 8Mps/L | 185EI/(L3) | 160m2m2=EI/(L3)*(1.5Mps/(Mps+2Mpm)+0.5) | V1=0.26R+0.12F V2=0.43R+0.19F |
| Elasto-Plastic Bending | 0.64 | 0.50 | 0.78 | 4(Mps+2Mpm)/L | 384EI/(5L3) | 0.39R+0.11F±Mps/L | ||
| Plastic Bending | 0.50 | 0.33 | 0.66 | 4(Mps+2Mpm)/L | 0 | 0.38R+0.12F±Mps/L | ||
| Plastic Membrane | 0.50 | 0.33 | 0.66 | 4Np/L | 2Npymax/L | |||
 |
Elastic | 0.58 | 1.00 | 1.73 | 8Mps/L | 185EI/(L3) | 160m2m2=EI/(L3)*(1.5Mps/(Mps+2Mpm)+0.5) | V1=0.375R V2=0.625R |
| Elasto-Plastic Bending | 0.64 | 1.00 | 1.56 | 4(Mps+2Mpm)/L | 384EI/(5L3) | 0.50R±Mps/L | ||
| Plastic Bending | 0.50 | 1.00 | 2.00 | 4(Mps+2Mpm)/L | 0 | 0.50R±Mps/L | ||
| Plastic Membrane | 0.50 | 0.33 | 0.66 | 4Np/L | 2Npymax/L | |||
 |
Elastic | 1.00 | 0.43 | 0.43 | 16Mps/(3L) | 107EI/(L3) | 106m2m2=EI/(L3)*(1.5Mps/(Mps+2Mpm)+0.5) | V1=0.25R+0.07F V2=0.54R+0.14F |
| Elasto-Plastic Bending | 1.00 | 0.49 | 0.49 | 2(Mps+2Mpm)/L | 48EI/(L3) | 0.78R-0.28F±Mps/L | ||
| Plastic Bending | 1.00 | 0.33 | 0.33 | 2(Mps+2Mpm)/L | 0 | 0.75R-0.25F±Mps/L | ||
| Plastic Membrane | 1.00 | 0.33 | 0.33 | 4Np/L | 2Npymax/L | |||
 |
Elastic | 1.00 | 1.00 | 1.00 | 16Mps/(3L) | 107EI/(L3) | 106m2m2=EI/(L3)*(1.5Mps/(Mps+2Mpm)+0.5) | V1=0.25R+0.07F V2=0.54R+0.14F |
| Elasto-Plastic Bending | 1.00 | 1.00 | 1.00 | 2(Mps+2Mpm)/L | 48EI/(L3) | 0.78R-0.28F±Mps/L | ||
| Plastic Bending | 1.00 | 1.00 | 1.00 | 2(Mps+2Mpm)/L | 0 | 0.75R-0.25F±Mps/L | ||
| Plastic Membrane | 1.00 | 1.00 | 1.00 | 4Np/L | 2Npymax/L | |||
 |
Elastic | 0.81 | 0.45 | 0.55 | 6Mps/L | 132EI/(L3) | 122m3m3=EI/(L3)*(2Mps/(Mps+3Mpm)+0.5) | V1=0.17R+0.17F V2=0.33R+0.33F |
| Elasto-Plastic Bending | 0.87 | 0.52 | 0.60 | 2(Mps+3Mpm)/L | 56EI/(L3) | 0.525R-0.025F±Mps/L | ||
| Plastic Bending | 1.00 | 0.56 | 0.56 | 2(Mps+3Mpm)/L | 0 | 0.52R-0.02F±Mps/L | ||
| Plastic Membrane | 1.00 | 0.56 | 0.56 | 6Np/L | 3Npymax/L | |||
 |
Elastic | 0.81 | 0.67 | 0.83 | 6Mps/L | 132EI/(L3) | 122m3m3=EI/(L3)*(2Mps/(Mps+3Mpm)+0.5) | V1=0.17R+0.17F V2=0.33R+0.33F |
| Elasto-Plastic Bending | 0.87 | 0.76 | 0.87 | 2(Mps+3Mpm)/L | 56EI/(L3) | 0.525R-0.025F±Mps/L | ||
| Plastic Bending | 1.00 | 1.00 | 1.00 | 2(Mps+3Mpm)/L | 0 | 0.52R-0.02F±Mps/L | ||
| Plastic Membrane | 1.00 | 1.00 | 1.00 | 6Np/L | 3Npymax/L | |||
| Load and Mass Distribution | Domain | Kl | Km | Klm | Rmax | kl | ke | V |
 |
Elastic | 0.40 | 0.26 | 0.65 | 2Mp/L | 8EI/(L3) | 0.69R+0.31F | |
| Plastic Bending | 0.50 | 0.33 | 0.66 | 2Mp/L | 0 | 0.75R+0.25F | ||
 |
Elastic | 0.40 | 1.00 | 2.50 | 2Mp/L | 8EI/(L3) | 0.50R+0.50F | |
| Plastic Bending | 0.50 | 1.00 | 2.00 | 2Mp/L | 0 | 0.50R+0.50F | ||
 |
Elastic | 1.00 | 0.24 | 0.24 | Mp/L | 3EI/(L3) | 1.74R-0.74F | |
| Plastic Bending | 1.00 | 0.33 | 0.33 | Mp/L | 0 | 1.50R-0.50F | ||
 |
Elastic | 1.00 | 1.00 | 1.00 | Mp/L | 3EI/(L3) | 1.00R | |
| Plastic Bending | 1.00 | 1.00 | 1.00 | Mp/L | 0 | 1.00R |
|
where: m1=EI/(L3)*(1.5Mps/(Mps+2Mpm)+0.25) m2=EI/(L3)*(1.5Mps/(Mps+2Mpm)+0.5) m3=EI/(L3)*(2Mps/(Mps+3Mpm)+0.5) |