Issue 53

R. M. Reda et al., Frattura ed Integrità Strutturale, 53 (2020) 106-123; DOI: 10.3221/IGF-ESIS.53.09

Two NSM Bars

One NSM Bar

Leg        Leg           angle   length     

Leg        Leg           angle   length      

1.60

1.60

45    50 45    100 45    150 60    50 60    100 60    150 90    50 90    100 90    150

45    50 45    100 45    150 60    50 60    100 60    150 90    50 90    100 90    150

1.50

1.50

1.40

1.40

1.30

1.30

P u /P u,θ=0

P u /P u,θ=0

1.20

1.20

1.10

1.10

(a)

(b)

1.00

1.00

50 0.8L                        0.5L                      0.25L 100 150

50 0.8L                        0.5L                      0.25L 100 150

0

0

NSM bar length (mm)

NSM bar length (mm)

Figure 10: The effect of NSM bar length on P u / P u, θ =0 for: (a) beams strengthened with one NSM bar and (b) beams strengthened with two NSM bars.

Two NSM Bars

One NSM Bar

Leg        Leg           angle   length      

Leg        Leg           angle   length      

3.00

3.00

45    50 45    100 45    150 60    50 60    100 60    150 90    50 90    100 90    150

45    50 45    100 45    150 60    50 60    100 60    150 90    50 90    100 90    150

2.50

2.50

2.00

2.00

1.50

Δ u /Δ u,θ=0

1.50

Δ u /Δ u,θ=0

1.00

1.00

0.50

0.50

(a)

0.00

(b)

0.00

0

50

100

150

0.8L                        0.5L                      0.25L

0

50 0.8L                        0.5L                      0.25L 100 150

NSM bar length (mm)

NSM bar length (mm)

Figure 11: The effect of NSM bar length on Δ u / Δ u, θ =0 for: (a) beams strengthened with one NSM bar and (b) beams strengthened with two NSM bars.

Two NSM Bars

One NSM Bar

Leg        Leg           angle   length      

Leg        Leg           angle   length      

1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10

1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10

45    50 45    100 45    150 60    50 60    100 60    150 90    50 90    100 90    150

45    50 45    100 45    150 60    50 60    100 60    150 90    50 90    100 90    150

E/E θ=0

E/E  θ=0

(b)

(a)

50 0.8L                        0.5L                      0.25L 100 150

50 0.8L                        0.5L                      0.25L 100 150

0

0

NSM bar length (mm)

NSM bar length (mm)

Figure 12: The effect of NSM bar length on E / E θ =0 for: (a) beams strengthened with one NSM bar and (b) beams strengthened with two NSM bars.

The effect of NSM bar length for the strengthened beams on maximum deflection with respect to maximum deflection of the corresponding beam but without end anchorage Δ u / Δ u, θ =0 were shown in (Fig. 11), the highest increasing in maximum deflection were for beam strengthened with one NSM bar of length 0.5L see (Fig. 11-a). The same observation in beams strengthened with two NSM bars with end inclination angle 60 º and 90 º see (Fig. 11-b). (Fig. 12) shows the effect of NSM bar length on the beams stiffness compared to the stiffness of the corresponding beams but without end anchorage E / E θ =0 , there are no noticeable changes in the stiffness of beams strengthened with one NSM bar when use different NSM bar length 0.8L, 0.5L and 0.25L see Fig (12-a).

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