Behavior of bonded and unbonded prestressed normal and high strength concrete beams

Peer review under responsibility of Housing and Building National Research Center.

Figures & data

Fig. 7a Test set-up.

Fig. 7b Test set-up of beam specimens.

Fig. 1 Concrete dimensions and cable profile of prestressed beams.

Fig. 3 The prestressing strand placed inside the polyethylene duct.

Fig. 4 Application of the prestressing force.

Fig. 5 Grouting process.

Table 1 Experimental program for beams.

Beams	Legend	$f_c^{’}\text{MPa}$	Prestre-ssing index	Strand area (mm)	Non-prestressed steel	Calculated force (kN)	Measured force (kN)	Elongation after losses (mm)	Bond
B1	B1-70-N-B	72	0	–	6T10	–	–	–	Bonded
B2	B2-70-P-B	75	0.70	99	2T10	105.6	100	22.22	Bonded
B3	B3-70-F-B	76	1.00	140	–	152.1	140	22.06	Bonded
B4	B4-100-N-B	95	0	–	6T10	–	–	–	Bonded
B5	B5-100-P-B	97	0.70	99	2T10	105.6	102	22.58	Bonded
B6	B6-100-F-B	94	1.00	140	–	152.1	142	22.15	Bonded
B7	B7-40-P-U	43	0.70	99	2T10	105.6	104	23.02	Unbonded
B8	B8-70-P-U	72	0.70	99	2T10	105.6	101	22.3	Unbonded
B9	B9-100-P-U	95	0.70	99	2T10	105.6	104	22.93	Unbonded

Where legend of the beams was as follows: Beam number-compressive strength-degree of prestressing-grout in the duct B – f_cu – fully (F) or partially (P) or without prestresing (N)- bonded (B) or unbonded (U).

Fig. 6 The calculated and measured prestressing stress along the beam span for Partially prestressed beam with compressive strength 72 MPa.

Fig. 2a Reinforcement details of non-prestressed beams.

Fig. 2b Reinforcement details of fully prestressed beams.

Fig. 2c Reinforcement details of partially prestressed beams.

Fig. 8 Cyclic loading pattern.

Fig. 9 Location of the different instrumentations.

Table 2 Experimental results.

Specimen	Pcr (kN)	Δcr (mm)	Py (kN)	Δy (mm)	Pmax (kN)	Δ at Pmax (mm)	Δu (mm)	Initial Stiffness (kN.mm/mm)	Post cracking Stiffness (kN mm/mm)	Failure mode
B1	33	2.54	103	16.8	152	140.7	140.7	6.70	5.525	A
B2	64	3.15	79	19.05	148	121.8	151	20.33	3.003	B
B3	70	3.57	83	19.88	135	63.2	63.2	18.63	2.856	C
B4	39	2.81	105	18.9	157	138	152	9.91	5.595	A
B5	67	3.56	81	19.8	153	112	121	22.07	3.451	B
B6	74	4.09	88	20.7	145	76	102	19.70	2.877	C
B7	47	4.07	115	29.2	141	76	91	12.71	2.928	B
B8	63	3.54	113	25.4	148	66	76	18.10	2.991	B
B9	65	3.6	121	24.8	155	53	70	20.96	3.561	B

(A) Yielding of steel reinforcement followed by crushing of concrete. (B) Yielding of non-prestressed steel followed by crushing of concrete then rupture of the prestressing strand. (C) Crushing of concrete followed by sudden collapse for the beam due to rupture of the prestressing strand.

Table 3 Ductility index.

Beam	Einel (kN/mm)	Eel (kN/mm)	Et (kN/mm)	Ductility index Ue	Ductility index μΔ = Δu/Δy
B1	16,551	1933	18,484	5.28	8.38
B2	16,468	4053	20,521	3.03	7.93
B3	3778	3247	7025	1.58	3.18
B4	21,380	1817	23,197	6.88	8.04
B5	15,348	2981	18,329	3.57	6.11
B6	8043	4670	12,713	1.86	4.93
B7	8538	2107	10,645	3.026	3.12
B8	4631	1846	6477	2.254	2.99
B9	5774	2707	8484	2.066	2.82

Fig. 10 Failure modes of tested specimens.

Fig. 11 Load deflection relationship for specimens B1-70-N-B, B2-70-P-B and B3-70-F-B.

Fig. 12 Load deflection relationship for specimens B4-100-N-B, B5-100-P-B and B6-100-F-B.

Fig. 13 Load deflection relationship for specimens B2-70-P-B and B8-70-P-U.

Fig. 14 Load deflection relationship for specimens B5-100-P-B and B9-100-P-U.

Fig. 15 Load deflection relationship for specimens B1-70-N-B and B4-100-N-B.

Fig. 16 Load deflection relationship for specimens B2-70-P-B and B5-100-P-B.

Fig. 17 Load deflection relationship for specimens B3-70-F-B and B6-100-F-B.

Fig. 18 Load deflection relationship for specimens B7-40-P-U, B8-70-P-U and B9-100-P-U.

Fig. 19 The measured and predicated load-deflection curves of tested beams.

Table

Beam	$p_{\text{max theo}}^{(1)}\text{KN}$	$p_{\text{max theo}}^{(2)}\text{KN}$	$p_{\text{max theo}}^{(3)}\text{KN}$	${\frac{P_{\text{max theo}}}{P_{\text{max theo}}}}^{(1)}$	${\frac{P_{\text{max theo}}}{P_{\text{max theo}}}}^{(2)}$	${\frac{P_{\text{max theo}}}{P_{\text{max theo}}}}^{(3)}$
B7	134	122	134	0.95	0.86	0.95
B8	140	130	140	0.95	0.88	0.95
B9	144	137	144	0.93	0.88	0.93

(1) ACI method; (2) Naaman method; (3) Lee method.