THE FOUR-HINGE METHOD OF ANALYSIS OF MASONRY ARCHES

STUDENT: PAVEL TROFIMOV

D08118499 DT024/4

SUMMARY OF WORK CARRIED OUT

I. Preliminary design

Figure 3 Segmental masonry arch

Figure 1 Force diagram Figure 2 Line of thrust

Table 1 Stresses in the arch

Due to self-weight

fm.min = 0.035 (N/mm2) , Tension

fm.max = 0.068 (N/mm2) , Compression

Allowable

ft.bond.MIN = 0.091 (N/mm2), Tension

fm.k = 10.7 (N/mm2), Compression

SUMMARY OF WORK CARRIED OUT

II. Theoretical analysis

ResultsModel 1 (Unreinforced) P = 2.4 kN

αB=64.97˚

βC=70.44˚

Model 2 (Reinforced) P = 68.4 kN

αB=64.97˚

βC=57.39˚Figure 6 Angles to hinges B&C

Figure 5 Collapse load Model 2Figure 4 Collapse load Model 1

SUMMARY OF WORK CARRIED OUT

III. Experimental

Figure 7 Experimental setup

Figure 8 Arch contruction

Figure 9 Abutment model 2

Figure 11 Model 1 test setupFigure 10 Abutment model 1

PROJECT FINDINGS

Figure 12 Failure mode, Model 1 Figure 13 Failure mode, Model 2

Table 2 Collapse load

Name kN

Model 1Exp. 9.58

Model 2Exp. 35.88

Model 1Theor. 2.36

Model 2Theor. 68.42

Figure 15 Tension zone

Figure 16 Compression zoneFigure 14 Load vs. displacement

SUMMARY OF WORK CARRIED OUT

IV. LUSAS Finite Element Analysis

Applied actions:

PMODEL 1 = 5.7 kN

PMODEL 2 = 20.0 kN

Figure 17 Isometric view, LUSAS model Figure 18 Maximum principal stresses (Model 2)

Table 3 Stresses LUSAS vs. allowable, Compression ‘-‘, Tension ‘+’

Name N/mm2

  ShearEpoxy ShearMasonry FlexureMasonry TensionSteel TensionEpoxy

Model 1LUSAS 0.24 (B) 0.78 / -0.92 (B)

Model 2LUSAS 2.91 (A-B) 0.84 (B) 2.70 / -3.50 (B) 8.99 (B) 0.01 (B)

Allowable 2.03 1.82 0.091 / -10.7 154 0.12

PROJECT FINDINGS• The formation of four-hinge mechanism does not necessarily lead to ultimate collapse but rather to SLS failure in

unreinforced masonry arches.

• In masonry arches reinforced with the near surface reinforcement, as examined, it’s likely to get a failure via debonding of reinforcement.

• Strengthening of the arch on the soffit with near surface reinforcement proves to provide a stiffer structure. It reduces deflections and, prevents crack formation and propogation.

• This form of strenghtening of masonry arches proves to inefficient, as it difficult to utilize the tensile properties of reinforcement at the hinges where it expected to be in tension.

• The four-hinge mechanism of failure is the mode of failure most likely to occur in the arch with a quarter-span point load, however, it has been shown in leterature that in 90% of the cases the presence of the fill responsible for the stability of the arch, thus it can result in a different mode of failure.

• Based on the limited models tested, the method of analysis to predict the collapse load for masonry arches must be treated with caution as it heavily relies on the assumptions such as: abutments are rigid and the four-hinge mechanism of failure is the only mode of failure allowed to develop.

Figure 19 Debonded reinforcement, tension zone. Figure 20 Debonded reinforcement, compression zone.

SUGGESTIONS FOR THE FUTURE RESEARCH

• The assumptions that abutments are rigid must be strictly adhered to, this can be done by ensuring no rotation is allowed in the reaction frame e.g. by providing spikes welded to the reaction frame to prevent the rotation of concrete abutment inside the casing.

• To investigate the behaviuor and the mode of failure of the arches further, presence of the fill must be considered.

• Different method of reinforcing the arch may be concidered in aim to achieve a full composite action between steel and masonry. This can be done by cutting grooves in the masonry and embedding steel bars inside the grooves which can provide for a larger contact area between steel and brick. Also, mechanical ancors may be considered either insitu or drilled to hold the steel in place.

• Provision of strain gauges on the reinforcing steel to record the stresses in the reinforcement during the testing. The attempt must be made to place the gauges where hinges are expected to form on the intrados.

• Different finite element modelling techniques may by investigated to approximate the real structure. Finite element model to simulate the cracked section can give more accurate results on the behaviour of the arch under load.

Figure 21 Abutment rotation.

THANK YOU

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