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Then in the code, you have a few details for talking back and forth between the push notification methods and the user interface, as well as the remote server. Here s what that looks like in the ViewController code:

The physical interpretation is the same as in the simply supported case. If we denote the lowest value of kL that satisfies Eq. (30.13) by (kL)cr, then the column buckling load is given by Pcr = EI(kL)2 cr L2 (30.14)

FIGURE 30.3 Column with ends fixed against rotation and an elastic end constraint against transverse deflection. (a) Undeflected column; (b) deflection curve; (c) freebody diagram of deflected segment.

Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.

+5V NCD-101-6

-(IBAction)handleSendButton:(id)sender { NSLog( @"handleSendButton" ); // make a get request to our script with the msg parameter set // msg=URLENCODEDSTRING; CFStringRef outString = CFURLCreateStringByAddingPercentEscapes(kCFAllocatorDefault, (CFStringRef)messageTextView.text, NULL, NULL, kCFStringEncodingUTF8); NSString *urlFormatString = @"http://2push2.us/apress/apress.php token=%@&cmd=msg&msg=%@"; NSURL *composedURL = [NSURL URLWithString:[NSString stringWithFormat:urlFormatString,deviceTokenField.text,(NSString *)outString]]; NSLog( @"composedURL:%@", composedURL ); NSString *result = [NSString stringWithContentsOfURL:composedURL];

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Since the column under consideration here has greater resistance to buckling than the case in Fig. 30.2e, the (kL)cr here will be greater than . We can therefore evaluate Eq. (30.13) beginning with kL = and increasing it slowly until the value of the left side of Eq. (30.13) changes sign. Since (kL)cr lies between the values of kL for which the left side of Eq. (30.13) has opposite signs, we now have bounds on (kL)cr. To obtain improved bounds, we take the average of the two bounding values, which we will designate by (kL)av. If the value of the left side of Eq. (30.13) obtained by using (kL)av is positive (negative), then (kL)cr lies between (kL)av and that value of kL for which the left side of Eq. (30.13) is negative (positive). This process is continued, using the successive values of (kL)av to obtain improved bounds on (kL)cr, until the desired accuracy is obtained. The last two equations in Eq. (30.12) imply perfect rigidity of the surrounding structure with respect to rotation. A more general result may be obtained by taking into account the elasticity of the surrounding structure in this respect. Suppose that the equivalent torsional spring constants for the surrounding structure are K(T, 0) and K(T, L) at x = 0 and x = L, respectively. Then Eq. (30.12) is replaced by y(L) = 0 M(0) = K(T, 0) dy(0) dx dy(L) dx (30.15)

M(L) = K(T, L)

Proceeding as before, with Eq. (30.15) replacing Eq. (30.12), we obtain the following equation for kL: L4K(0)K(T, 0)K(T, L) L3 3 [K(T, 0) + K(T, L)]K(0) EI(kL) (EI)2 (kL)3 + LK(T, 0)K(T, L) EI(kL) K(0)L2 + (kL) EI(kL) L sin kL

+5V NCD-101-7

+ K(T, 0) + K(T, L)

NSLog( @"result:%@", result ); CFRelease(outString); } -(void)handleSetDeviceTokenField:(NSString *)inDeviceToken { NSLog( @"handleSetDeviceTokenField:%@", inDeviceToken ); deviceTokenField.text = inDeviceToken; } -(void)handleDidReceiveRemoteNotification:(NSDictionary *)userInfo { NSDictionary *aps = [userInfo valueForKey:@"aps"]; NSString *alert = [aps valueForKey:@"alert"]; messageTextView.text = alert; } And in the App Delegate where we interact with the notifications, here are the three key methods: - (BOOL)application:(UIApplication *)application didFinishLaunchingWithOptions:(NSDictionary *)launchOptions { // register for remote notifications UIRemoteNotificationType types = UIRemoteNotificationTypeBadge | UIRemoteNotificationTypeSound | UIRemoteNotificationTypeAlert; [application registerForRemoteNotificationTypes:types]; // because we implement didFinishLaunchingWithOptions, the "old" entry method doesn't get called [self applicationDidFinishLaunching:application]; return YES; } - (void)application:(UIApplication *)application didRegisterForRemoteNotificationsWithDeviceToken:(NSData *)deviceToken { NSLog( @"didRegisterForRemoteNotificationsWithDeviceToken:%@", deviceToken ); NSString *inDeviceTokenStr = [deviceToken description]; NSString *tokenString = [inDeviceTokenStr stringByTrimmingCharactersInSet:[NSCharacterSet characterSetWithCharactersInString:@"< >"]]; tokenString = [tokenString stringByReplacingOccurrencesOfString:@" " withString:@""];

L3 [K(T, 0) + K(T, L)]K(0) cos kL EI(kL)2 +2 L4K(0)K(T, 0) + K(T, L) (1 cos kL) = 0 (EI)2(kL)4 (30.16)

The lowest value of kL satisfying Eq. (30.16) is the (kL)cr to be substituted in Eq. (30.14) in order to obtain the critical load. Here there is no apparent good guess with which to begin computations. Considering the current accessibility of computers, a convenient approach would be to obtain a plot of the left side of Eq. (30.16) for 0 kL < , and if there is no change in sign, extend the plot up to kL = 2 , which is the solution for the column with a perfectly rigid surrounding structure (Fig. 30.2c).

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