Part 3: Punching shear failure

Transcription

1 Part 3: Punching shear failure 1. What it is punching failure? 2. Presumed shape and geometry. 3. Condition of reliability? 4. Which structures are in danger? 5. How protect structures against punching shear failure? Punching of a pad (punching shear failure) Is well known firstly by slabs supported by columns. There is a lot of real cases by these kind of the structural failure. E.g. Disaster wedding video. 1

2 Punching of a pad Punching of a pad = punching shear failure) Can occur first of all by thin RC footings pads. There were done a lot of investigations, modelling and field test with the target to find relevant failure model and to formulate conditions of the punching action and the resistance of a structure. By different codes there are two main approaches to this problem: 1. Solution in the same manner as by the point supported slabs. 2. Usage of simplified technique as by foundation there are more uncertainties there (soil behaviour). Punching of a pad (results of field test of punching shear failure shape and circumstances of punching shear failure) Varies: shape of a pad, R zd, reinforcement. Was deduced, the shape angle of the first, most important crack is 45 or less. Sometime occurs failure in the contact area column pad. 2

3 Punching of a pad (presumed shape and conditions of punching shear failure) The condition of reliability commonly is simple v Rdc v Ed The main problem is how to find these booth quantities? v Ed is specific (factored) value of the shear force per 1m of control perimeter. This perimeter is defined differently by different codes: This stress is effective for punching, only. The figure is not fully correct as the control perimeter by EC2 can be everything between d and 2d for high loaded pads it is recommended to take d. And besides control perimeter must be defined resisting perimeter = critical perimeter rectangular - rounded Punching of a pad (presumed shape and conditions of punching shear failure) Firstly we need to calculate the punching force V Ed, which is a part of column s N Ed. Effective area is outside the chosen perimeter on the fig is for perimeter 2d, A ef filled with green. So: V ed = N ed - p d. A ef When we factorise V ed /u where: u is Control perimeter by this model we obtain factorised v ed [kn/m]. This can be compared with factorised v Rdc [kn/m]. Prior to learn this is important question how to express p d and influence of M ed in the foot of column? 1. Simplified, in the same manner like by flexure. (action force is dispersed by (L-2e) * B area, only. 2. Usage of the full theory adopted from slabs punching. 3

4 Punching of a pad - punching action according to EUROCODE 2: The theory By pressure the influence of the bending moment acting in the foot of column must be expressed. By EC2 is parameter used: = 1 + Δv/(V Ed /ui) = 1 + Δvui /V Ed In principle, Δv can be calculated from simple statics, with usage of the moment transferred between the slab and the column. But much more simple (and recommended) is to use the same technique and the same value as by flexure where the influence of M is expressed by increased value of p d due to decrease of A to A ef, see the figure and previous theory. And it is aviable!! Simplified - flexure p z = s z - q z Punching of a pad (punching shear failure) resistance of the structure For high loaded pads a=d is recommended, so critical perimeter is in the distance d/2 (figure). Sometimes critical perimeter as counter of the column is checked. Remaining quantities in the formula - see regular shear design k = 1+ ( /d) size factor etc.. 4

5 How to increase the pad resistance against punching? - increase the pad height h d. - increase the concrete strength class. - use stepped or slope pad (as last). - Use more flexural or add special reinforcement (it is not recommended) reinforcement against punching. Fig a)b)c) (a) 0) Another example of special anti-punching reinforcement 5

6 What about SUW? Punching failure cannot occur by Footing strips under a wall (SUWs) from structural point of view. There is no point support present. Moreover, strips under a wall a usually less stressed when compared to pads. By high load should be strip checked as a transversal beam with the breath of 1 m and height of the strip h. See Fig. Regular beam condition V Rdc V ed [kn] should be checked. g If V Rdc < V ed (never seen by SUW), increase the height or concrete strength or both. Theoretically can be attached with a shear reinforcement like a beam. Punching failure cannot occur by plain concrete pad due to the fact potential controlled perimeter lays outside the plan projection see fig. PC pads are less loaded (otherwise will be too huge) and its presumed failure is presumed by Principal tension, only. It is solved by previous formula: 0,85 h f /a (3p d /f td,pl ) 0,5 See previous lecture. What about PC Pad? 6

7 End of the design of Simple spread footings! Thank You for the attention! Unused slides follow 7

8 Punching of a pad (punching shear failure) Is well known firstly by slabs supported by columns. There is a lot of real cases by these kind of structures. E.g. Disaster wedding video. How to solve the punching issue by footing pads? (punching shear failure) By footings is the principle same but there are some important differences here: 1. The influence of bending M is expressed differently. See previous slide. 2. Footings are thicker when compared to slabs. 3. By footings it is strongly recommended to change the design of them, not to use special reinforcement. By Eurocodes is punching of footings not solved into details, now. Two major ways can be seen: A) Usage of the full theory used for slabs.(with lace problems) B) Usage of simplified techniques for verification of not punching, only. By this example is presumed the critical (control) perimeter should be find in the distance between (d, 2d). But the ratio H/B is absolutely outside the recommended range see next slide. 8

9 Simplified technique for punching review designed by lecturer Presumptions: Influence of bending moment is expressed by increased p d. The punching force is calculated from part of the area A eff outside the control perimeter. The area is reduced by 2e d (as usual) or not. The control perimeter is in the distance of d outside the column plan contour. For the resistance calculation v Rdc are used Eurocode principles and rules valid for shear (there are in the principle equal with punching). 9

10 Footing strip under a wall difference to a pad A pad is bended in both perpendicular directions x and y. A strip under a wall is bended in the direction x only can be solved as a pad (strip) with breath of 1 m. (The wall is stiff in its plane y-z.) This is valid both for geotechnical and structural design! The material of the wall implies the rigidity of the wall masonry connection and the character of contact and upward pressure distribution shape. masonry wall RC wall 10

11 Footing strip under a row of columns Field of usage: - when the pads tend to be too large (weak soil, high load), - when limiting of the differential settlement is necessary, Geotechnical design of a footing strip under a row of columns in simplified variant is similar technique to a pad used. Force quantities in Sumas are used e d(i) =( ΣM d(i) + ΣH d(i). H)/ (ΣN d(i) + Z d ) s z(i) =(ΣN d(i) + Z d )/(B. (L-2e d(i) )) R d For i = 1,2, 3 How to solve the punching issue by footing pads? (punching shear failure) By footings is the principle same but there are some important differences here: 1. The influence of bending M is expressed differently. See previous slide. 2. Footings are thicker when compared to slabs. 3. By footings it is strongly recommended to change the design of them, not to use special reinforcement. By Eurocodes is punching of footings not solved into details, now. Two major ways can be seen: A) Usage of the full theory used for slabs.(with lace problems) B) Usage of simplified techniques for verification of not punching, only. By this example is presumed the critical (control) perimeter should be find in the distance between (d, 2d). But the ratio H/B is absolutely outside the recommended range see next slide. 11

12 Geotechnical design of a footing pad Z d Self-weight of the pad + backfill + relevant part of the floor slab + blinding concrete (if used) N d Axial force from the superstructure (more loading cases possible) M d Bending moment in the foot of actual column (more loading cases possible) H d Horizontal force in the foot of actual column (more loading cases possible) B, L Plan dimensions of the pad A ef Effective contact area e d (e)= ( M d + H d. H)/ (N d + Z d ) A ef = (L-2 e d ). B Contact pressure s z s z = (N d + Z d ) / ((L-2 e d ). B) Equivalent forces scheme 12