# Free edges the treatment of free edges can be

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Free edges The treatment of free edges can be illustrated with an example. Example 2 Simple approach Try q q q q x y 2 . 0 8 . 0 Evidently the ‘y’ strips cause no difficulties as they span from the boundaries AB to DC. However for ’x’ strips, there is no obvious support at BC. This causes problems, unless a concentrated strip (i.e. beam) along BC is postulated. A B D C a y x q a loading = u.d.l. = q Figure 9
CVE80004 Advanced Concrete Design Strip Method for Slab Design Swinburne University of Technology 2017 Page 13 of 24 Hence the approach must be a bit more sophisticated. Near edge BC, all load transfer is likely to be in the ‘y’ direction; thus assume a width b=a/2 (say) in which one way action only occurs. A B D C a/2 q = q a a/2 q = 0 x y q = 0.8q q = 0.2q x y Figure 10 0.2q a/3 L.H. 'Y' Strip 2 = 0.0083 qa 2 2 3 .0.2q. 2 a 1 3 .0.2q (reaction) 0.8q q + .0.2q 1 3 M = 1 2 0.2q 3 a 2 M = ma 1 9 .0.1qa = 0.011 qa 2 2 M = 1 8 .0.8qa = 0.1 qa 2 2 M = 1 8 . (1.067)qa = 0.133 qa 2 R.H. 'Y' Strip 2 x-strip Figure 11
CVE80004 Advanced Concrete Design Strip Method for Slab Design Swinburne University of Technology 2017 Page 14 of 24 Strip approach a/2 M = 0.0083 qa a/2 x 2 + y M = 0.133 qa 2 + M = 0.011 qa x 2 + y M = 0.1 qa 2 + Figure 12 q = 0 q = q x y q = q q = 0 x y 2 2 1 1 3 3 a/4, say Figure 13
CVE80004 Advanced Concrete Design Strip Method for Slab Design Swinburne University of Technology 2017 Page 15 of 24 a/4 = max q 1 1 q 2 2 3 3 varies R R 3 3 worst case R R qa 4 = 0.063 qa 2 = 2 0.125 qa 0.188 qa (total) 2 2 M = qa max 1 8 2 = 0.125 qa 2 M = q 1 8 2 a 4 2 R = (max) qa 8 (max) a 4 . qa 8 Figure 14 a/4 M = 0.125 qa y 2 + x M = 0 + M = 0.188 qa y 2 + x M = 0.0078 qa 2 + A conservative design Figure 15
CVE80004 Advanced Concrete Design Strip Method for Slab Design Swinburne University of Technology 2017 Page 16 of 24 Point and strip loads and supports In order to handle point supports, Hillerborg postulated a two-dimensional twisting element to augment the bending strip. However, this complicates the essentially simple method very greatly. Concentrated actions can be handled within the confines of the simple strip method when it is realised that in practice there are no truly knife edge or ponit actions and that all are distributed over a finite area. Highly concentrated actions are also more likely to be critical in shear, rather than bending, so that the bending moment distribution alone is unlikely to b critical in the region of the concentrated action. The simpler approach to use for this type of action is to attempt to spread the action over a larger ara of slab quickly, as indicated in the following examples. An alternative approach has also been suggested [Kemp, K.O., Struct, Engr., 49, 543- , 1971] Example 3 Wall load Load carrying direction Heavily reinforced strip D t + D, say t Figure 16
CVE80004 Advanced Concrete Design Strip Method for Slab Design Swinburne University of Technology 2017 Page 17 of 24 Example 4 A better approach is to imagine a series of “secondary” strips perpendicular to the main strips and their bending action replacing the concentrated load by a patch load.