short: Short Column Function
View source: R/testfunctions.R
| short | R Documentation |
Short Column Function
Description
The short column function is defined by
f_{\rm short}(x) = 1 - \frac{4M}{b h^2 Y} - \frac{P^2}{b^2 h^2 Y^2}
with x = (Y, M, P).
Usage
short(x, b = 5, h = 15)
shortGrad(x, b = 5, h = 15)
Arguments
x |
a numeric |
b |
width of the cross-section in |
h |
depth of the cross-section in |
Details
The short column function describes the limite state function of a short column with uncertain material properties and loads.
| Input | Distribution | Mean | Standard deviation | Description |
Y | \mathcal{LN} | 5 | 0.5 | yield stress in \rm MPa |
M | \mathcal{N} | 2000 | 400 | bending moment in \rm MNm |
P | \mathcal{N} | 500 | 100 | axial force in \rm MPa |
The bending moment and the axial force are correlated with \rm{Cor}(M, P) = 0.5.
Note, \mathcal{N} represents the normal distribution and \mathcal{LN} is the log-normal distribution.
Value
short returns the function value of short column function at x.
shortGrad returns the gradient of short column function at x.
Author(s)
Carmen van Meegen
References
Kuschel, N. and Rackwitz, R. (1997). Two Basic Problems in Reliability-Based Structural Optimization. Mathematical Methods of Operations Research, 46(3):309–333.
Surjanovic, S. and Bingham, D. (2013). Virtual Library of Simulation Experiments: Test Functions and Datasets. https://www.sfu.ca/~ssurjano/ (retrieved January 19, 2024).
