Respondents’ Policy Suggestions

CHAPTER 3 COLLAPSE OF MASONR y BUTTRESSES

Depending on the form of the wall and the interlocking of the masomy, the cross-wall could be an effective part of the buttress, as in Figure 3 .9( d), or the wall could be completely ineffective in contributing to the resistance of the buttress, as in Figure 3.9(a). The fracture patterns in Figures 3.9(c) and 3.9(d) are derived from the assumption of a linear compressive stress distribution in a T-section, as illustrated in Figure 3.8 on the previous page. The fracture forms initially in the wall when the pressure point reaches the kern point of the T -section. Once the fracture surface leaves the wall, the buttress section is rectangular and the pressure point acts at the one-third point of the effective section.

(a)

(b) Hb

0 (a) (b)

Effective region of buttress

He (c)

He Hd

(c) (d)

Plan view Elevation views

Figure 3.9. Possible contributions of cross-walls to buttress, ranging from none (a) to greatest (d).

CHAPTER 3 COLLAPSE OF MASONRY BUTTRESSES

static friction between blocks to a level typical of stone on stone, and thus to prevent sliding. The buttresses were loaded laterally to collapse by slowly increasing the applied horizontal load. A rectangular buttress and aT-shaped buttress were tested, each with a height of 72.8 cm and a width of 18.2 cm. Each buttress was tested alone as in Figure 3.1 O( a), and tested again with an imposed load of 500g (11 %-14% of buttress weight) on top of the buttress to model the stabilising contribution of the weight of the arch as in Figure 3.1 O(b). In each case, failure occurred by oveliurning, with a fracture in the lower region of the buttress. Further details on the experiments are presented in Appendix B, including the predictions of the collapse mechanisms for each experiment.

Figures 3.10 and 3.11 present each buttress after collapse has occUlTed by oveliurning.

(a)

v=o

Figure 3.10. Test on rectangular buttress with htlb=4 and p=0.5 with a solid line for the fracture predicted by the method of section 3.6. The horizontal load is applied from the left by the white string, and the buttress is shown in the post-collapse configuration after it has reached its

CHAPTER 3 COLLAPSE OF MASONRY BUTTRESSES

Ca) V=O Cb) V=500g (1\ % of buttress weight)

Figure 3.11 Test on T-shaped buttress with htlb=4 and IFO.5 with a solid line for the predicted fracture.

The horizontal load is applied from the left by the white string, and the buttress is shown in the post-collapse configuration after it has reached its maximum capacity.

Test Number B27.S.0 B27.S.S00 T27.S.0 T27.S.S00

Vertical load, V v=o V=500g v=o V=500g

Theoretical H=667g H=955g H=1023g H=1279g

prediction of (~0.72) (~=O.62)

thrust, HII

Experimental H=710g H=920g H=980g H=1230g

Result, _{H lesl}

Tiu'ust to 878g 1128g 1360g 1596g

overturn solid buttress, Hs

H,lHfesf 0.94 1.04 1.04 1.04

Table 3.1 Expenmental results versus calculated results for model buttresses.

CHAPTER 3 COLLAPSE OF MASONRY BUTTRESSES

For the rectangular buttress and the T-shaped buttress, the experiments verified the predicted location of fracture based on a linear distribution of stress in·compression. In each case, the predicted value of collapse load was within approximately 6% of the actual collapse load: see Table 3.1. In real buttresses, as in the experiments, the joint patterns in the masomy determine the location of the fracture. These simple experiments have verified the existence of the fracture and illustrated that the straight fracture line resulting from a linear stress distribution provides a reasonable approximation of the collapse load of actual masomy buttresses under horizontal load.

As postulated in the theory presented in this chapter, the experiments demonstrated that blocks not held in direct compression will simply drop from the effective mass of the buttress. The failure is not characterised by sliding or by failure of the individual blocks, but rather by opening of the joints between masomy blocks. The buttress remains essentially vertical as the applied load is increased, and at the point of maximum horizontal load, the buttress separates into two sections: the effective mass of the buttress, and the ineffective wedge of material that does not contribute to the stability of the buttress. Failure occurs by overturning as illustrated in Figures 3.10 and 3.11.

Dozens of additional experiments on model buttresses of varying sizes gave similar results, though only four such experiments have been presented here. The experiments provide support for the theory developed in this chapter, though futiher experiments are necessary to verify the limits to the theory presented here.

3.9 Summary

The methods presented in this chapter provide a straightforward approach to predicting the collapse load for horizontal buttresses under lateral load. This chapter has presented several key ideas:

1.) The horizontal thrust of an arch or vault acts to de-stabilise a masomy buttress, while the veliical forces act to stabilise the buttress. Methods to assess buttress capacity against overturning forces should focus on the value of the horizontal thrust.

CHAPTER 3 COLLAPSE OF MASONRY BUTTRESSES

2.) The overturning collapse of a masomy buttress involves the formation of a surface of fracture, which reduces the collapse load by reducing the stabilising moment of the buttress. Horizontal thrusts calculated on the basis of an assumed monolithic buttress are unsafe.

3.) The surface of fraCture can be calculated by assuming a linear distribution of compressive stress and by supposing that a crack forms when the resultant internal force exits the kern of the section (middle-third for rectangular cross-sections). The problem is statically determinate and involves the solution of two equations with two unknowns, representing the thrust and fracture height.

4.) Based on these assumptions, the fracture surface at collapse is planar for rectangular buttresses. This result can be observed in actual buttresses at collapse due to overturning.

5.) In real buttresses the fracture depends on the composition of the masomy, and the planes of failure are likely to make a zig-zag line along the existing joint surfaces. The method of straight-line fracture presented in this paper gives an approximate solution to the problem. Complex buttress forms require additional simplifying assumptions or more complex analysis.

6.) Adjacent veliical walls may contribute greatly to the buttress stability and should be considered in the case of buttresses combined with cross walls. The engineer must judge the contribution of the cross walls based on the interlocking of masomy blocks in each particular case.