Shear stressed masonry wall

Transcription

1 Facuty o Architecture Chair o Structura Design N:\Lehre\ACCESS\0\04-Skript\08-Mann-Mueer.doc Contact: Dr. Bakeer Dr.-Ing. Teephone/Fax: +49 (0) /-3773 Tammam Bakeer Emai: Tammam.Bakeer@TU-Dresden.de Dresden, 05 Juy 0 Shear aiure o Masonry Theory o Mann-Müer. Introduction A shear pane, Figure is subjected to vertica and horizonta orces. Loads acting perpendicuary o the wa are not considered. I an eement is cut out o the pane, then the stress in a vertica direction is at a our boundaries the shear stresses are. Horizonta compressive stress is negigiby ow. The aiure theory predicts at which stress coupe vaues o and at which the aiure can be expected. N V Figure Shear stressed masonry wa The known aiure hypotheses or homogenous materias attempt to attribute the materia aiure to a singe speciic condition, or exampe, exceeding the acceptabe principa tensie stress or the shear stress. The aiure hypotheses cannot be unrestrictedy appied to masonry. Firsty, masonry is not homogeneous, but is aected by the joints. Secondy, it is

2 Facuty o Architecture Chair or Structura Design Memo dated 05 Juy 0 made up o numerous eements, namey the bricks and bed and vertica joints, a o which can ai individuay, and each or dierent reasons. It is not thereore possibe to attribute shear aiure to a singe cause, or exampe riction aiure o the bed joint; on the contrary, many types o aiure are possibe. They must be deduced rom a sma section o the masonry and the most unavorabe type o aiure is decisive. As we as riction in the bed joint, the tensie and compression strength o the bricks and their ormat o importance.. Assumptions The bonded brickwork o a cut-out specimen as shown in Figure is considered. The theory is based on the inding that no shear stresses can be transerred in the vertica joints between the bricks. That is to say, there is no oad present in these vertica joints which coud produce riction. Furthermore, these joints are oten not propery ied with mortar, or the mortar cracks due to shrinkage. This inding is conirmed by the observation that shear cracks neary aways originate at the vertica joints. On the other hand, shear stresses act in horizonta joints. They produce torque in the individua brick, Figure. Equiibrium can ony be attained via a vertica orce coupe, this coupe inuence the vertica stresses in such manner that the one brick ha is subjected to arger stresses, and the other brick ha is subjected to smaer stresses, rom equiibrium it oows that h = where = and + = 3. Faiure criteria = + and Faiure can occur in various ways, depending on the reationship o via. 3.. Faiure due to the bed joint cracking open () = () For every sma vertica stresses, the ower stress, according to Eq.() becomes tensie stress. I the tensie strength o the mortar is thus exceeded, aiure occurs. / Figure b h / / Cacuation diagram / /

3 Facuty o Architecture Chair or Structura Design Memo dated 05 Juy 0 t t + h ( ) (3) (4) 3.. Friction aiure o the bed joint According to the riction aw, the brick ha subjected to the esser stress wi ai earier than the brick ha subjected to M + µ (5) From Eq.() & Eq.() h = (6) I one inserts rom Eq.(6) and soves or, then the aiure criteria can be ormuated as µ + h h (7) + µ + µ Or with reduced cohesion and reduced riction coeicient µ. + µ (8) = + µ µ µ = + µ h h Thus the actua coeicient and µ which represent the reduction o to are not the determinative actors or the riction aiure but the reduced coeicients and µ. This is unmistakaby conirmed by numerous tests. Figure 3 shows the reduction. The observed deveopment o cracks in stepped orm as shown in Figure 5 is expained by the act that the brick haves with the smaer stress, are each positioned diagonay opposite one another. Couomb (9) (0) Reduced riction ine Figure 3 Reduced riction ine 3

4 Facuty o Architecture Chair or Structura Design Memo dated 05 Juy 0 Figure 4 (a) (a) shear aiure o the bed joints, (b) Faiure due to cracking o the bricks (b) 3.3. Faiure due to cracking o the bricks When arger imposed oad is appied, the riction aiure in the horizonta joint does not occur because the brick cracks irst. Since it is assumed that no shear stresses can be transerred in the vertica joints, the bricks must transer the doube shear orce in every second course. Thus cracking o the bricks can occur. More precise testing o an individua brick with regard to the easticity theory has shown that the stresses, xst =, yst = 0 and st =. 3 occur at the centre o the brick. The brick cracks as soon as this incined principa tensie stress I in the brick exceeds its strength bz. I = + ( ) + (.3 ) bz () ( + bz ) ( ) + (.3 ) () bz + bz (.3 ) (3).3 bz + bz This criterion is given in igure 6 by paraboa. Figure 4b shows such a aiure. The cracks aways originate at the vertica joints and are sighty incined according to the direction o the incined principa stresses within the brick. It shoud be particuary noted that the principe incined tensie stresses in a homogeneous wa so reect exacty the aiure condition which occurs in masonry wa. Whereas in a homogeneous wa xy = yx =, the shear stress in bricks max st =. 3 produces in the masonry wa, as shown, increased principa stresses and thereore aiure occurs sooner. (4) 4

5 Facuty o Architecture Chair or Structura Design Memo dated 05 Juy 0 Figure 5 (a) (a) FE Mesh and Loads on Brick, (b) Resuts rom ANSYS (b) 3.4. Compression aiure o the masonry wa Compression aiure occurs with very high stresses, namey when the brick ha subjected to the arger stress, according to Eq.() attains the compressive strength o the masonry k that is when = k. k k h ( ) 4. Enveoping curve xy = yx In igure 6 the acceptabe shear stresses according to the aiure criteria are given reated to. A vaues o there under are acceptabe, a higher vaues cause aiure. With a ow vaue riction aiure occurs, which is imited by the paraboa or cracking o the brick. In the extreme case, the paraboa (c) can ie competey under ine (b), namey or bricks with very ow tensie strength, or exampe. Lightweight hoow bocks combined with mortar with very good cohesion. It shoud be particuary noted that a these aiure oads can occur on was with rectanguar cross-sections as we as composite cross-sections. The undamenta principe that shear stresses are aways equa in coupes, that is =, is aso vaid or rectanguar crosssection, so that there aso cracking may occur, as proved in numerous tests. The dierence is ony the distribution o the stresses. (5) (6) 5

6 Facuty o Architecture Chair or Structura Design Memo dated 05 Juy 0 (b) Friction aiure o the bed joint (c) Cracking o the bricks (a) Bed joint cracking open bz β zst t β HZ β vk HS 0 arctan( µ ) No Faiure (d) Compression aiure k β M Figure 6 Faiure enveop curves 5. Reerences. Mann, W. & Müer, H.: Schubtragähigkeit von Mauerwerk. Mauerwerk-Kaender, 3 (978), pp Mann, W. & Müer, H.: Faiure o Shear-Stressed Masonry- an Enarged Theory, Tests and Appication to Shear Was. Proceedings o the British Ceramic Society, 30 (98), pp Mister, M.: Verormungsbasiertes seismisches Bemessungskozept ür Mauerwerksbauten. PhD-Thesis, Technischen Hochschue Aachen, 006. Technischen Hochschue Aachen: Aechen, Deutschand 006 6