Newmark-β Method has time step methods in its formaultion similar to other numerical methods. It introduces two parameters, β and . For numerical stability of the solution, both β and should have certain values. is always taken as 1/2, while β can be taken as 1/4 or 1/6. If β is taken as 1/4, the method is called the Constant Acceleration Method and if β is taken as 1/6, the method is called the Linear Acceleration Method.
The incremental equations of the Newmark - β Method can be written as,
Eq. 5.2.1
Eq. 5.2.2
After setting to 1/2,
Eq. 5.2.3
Eq. 5.2.4
Newmark - β Triangular Load Calculator
m = 0.2 kip.s²/in
k = 10 kip/in
ζ = 0.05
Fₒ = 20 kips
t₁ = 0.02 sec
td = 0.06 sec
Time t = 1.5 sec
Output | |
---|---|
Maximum Displacement | 0.00 in |
Maximum Velocity | 0.00 in/s |
Maximum Acceleration | 0.00 in/s2 |