MATLAB Examples

## Example with a single span suspension bridge

No coupling is introduced here, to keep calculations simple.

```clear all;close all;clc; ```

## Get the structural properties of the bridge

```run('LysefjordBridge.m'); ```

## Get the eigen-frequencies and mode shapes

call of the function "eigenBridge".

```Ncoef= 20; [wn,phi,~] = eigenBridge(Bridge,Ncoef); % wn: eigen frequencies (rad/s) % phi: mode shapes of the deck ```

## Lateral static response

```clear Wind Wind.U = 20; % mean wind speed Bridge.DOF = 'lateral'; % eigen frequencies computed previously for lateral component Bridge.wn = wn(1,:); % mode shapes computed previously for lateral component Bridge.phi = squeeze(phi(1,:,:)); [Dox] = staticResponse(Bridge,Wind); figure hold on plot(Bridge.x.*Bridge.L,Dox) xlim([0,Bridge.L]); xlabel('span (m)'); ylabel('Lateral static displacement (m)');box on set(gcf,'color','w'); ```

## Vertical static response

```clear Wind Wind.U = 20; % mean wind speed % modification of Input: Bridge.DOF = 'vertical'; % eigen frequencies computed previously for lateral component Bridge.wn = wn(2,:); % mode shapes computed previously for lateral component Bridge.phi = squeeze(phi(2,:,:)); [Doz] = staticResponse(Bridge,Wind); figure hold on plot(Bridge.x.*Bridge.L,Doz) xlim([0,Bridge.L]); xlabel(' span (m)'); ylabel('Vertical static displacement (m)');box on set(gcf,'color','w'); ```

## Torsional static response

```clear Wind Wind.U = 20; % mean wind speed Bridge.DOF = 'torsional'; % eigen frequencies computed previously for lateral component Bridge.wn = wn(3,:); % mode shapes computed previously for lateral component Bridge.phi = squeeze(phi(3,:,:)); [Dot] = staticResponse(Bridge,Wind); figure hold on plot(Bridge.x.*Bridge.L,180/pi.*Dot) xlim([0,Bridge.L]); xlabel(' span (m)'); ylabel('Torsional static displacement (^o)'); legend('Dot','location','south') box on set(gcf,'color','w'); ```

## Torsional static divergence (Ucr = 188 m/s)

```U = linspace(0,188,100); Dot_torsDiv = zeros(numel(U),Bridge.Nyy); for ii=1:numel(U), Wind.U = U(ii); % mean wind speed [Dot_torsDiv(ii,:)] = staticResponse(Bridge,Wind); end figure plot(U,180/pi.*Dot_torsDiv(:,15)) ylim([0,10]); xlabel(' U (m/s)'); ylabel('Torsional static displacement (^o)'); box on set(gcf,'color','w'); ```
```Ucr = 188 m/s. Static torsional divergence is reached ```