2.1. Proposed structure configuration and dimensions

The basic structural system is illustrated in Figure 1 (section) and Figure 2 (elevation). The house uses bamboo roof trusses at 4-ft (1.22-m) centers that are supported by bamboo braced frames. The frames are supported by 3-ft (0.9-m) high masonry plinth walls, which are composed of concrete masonry units (CMUs) made from recycled concrete rubble. The masonry plinths raise the bamboo frames above ground to protect them from ground moisture and rain splash.

Figure 1. Section (courtesy B. King).

Figure 2. Elevation (courtesy B. King).

The braced bamboo frames are assembled on the ground, then raised into place and set onto the previously constructed masonry plinth walls. Lath and plaster (or wattle and daub) is applied to the bamboo framing. To protect the bamboo from moisture in the plaster, the lath is held off the bamboo frames using recycled bottle caps as spacers. Bamboo roof trusses are built onsite, and set into place bearing on the top member of the braced frames. Purlins may consist of nominal 1-in. by 4-in. (25.4-mm × 50.8-mm) boards spaced approximately 8-in. (101.6 mm) apart are used to support a corrugated sheet metal roof. Sheet metal roofs are often used in Haiti. Since the roof functions as a diaphragm for resisting lateral loads, diagonal bracing may be needed to provide sufficient capacity for larger diaphragm spans.

The 3-ft. (0.9 m) high CMU plinth wall is supported on a continuous strip footing. The CMU blocks are fabricated on site by hand-tamping a concrete mix into metal molds. A low-strength concrete made using crushed concrete rubble as aggregate is used (approximately 300 psi (2 MPa) compressive strength at 3 days), to minimize cement content. The CMU plinth wall is not load bearing, but serves as a form for cast-in-void reinforced concrete. Within select CMU cells where the bamboo frame columns attach, a No. 3 deformed rebar runs continuously from the foundation within mortar-filled CMU cells. The bamboo frame is held approximately 2- to 3-inches (50 to 75-mm) above the CMU plinth walls, exposing the No. 3 rebar and creating a ductile connection, which is the focus of this paper. After the braced frame has been lowered onto the rebar, the bamboo culm containing rebar is filled with mortar by injection through a small hole in the culm wall by means of a grout bag.

A capacity design principle was utilized to provide lateral resistance to earthquake loading. The intended mechanism consists of plastic hinging within the short length of exposed rebar. Hinging of the rebar limits the forces that can be developed at the connections within the bamboo frame, allowing the frame to be designed to remain elastic. To protect the 2-in. (50-mm) exposed rebar from corrosion, the top of a plastic bottle is slipped over the exposed rebar and embedded in the CMU plinth mortar during construction of the masonry wall. The bamboo culm is placed on top of the plastic bottle top, enclosing the protruding rebar, while preventing subsequently applied mortar from leaking out of the base of the culm.

2.2. Low-strength concrete mix design

Low-strength concrete mix designs were developed for use in making the CMUs. Experiments were conducted using Type I Portland cements sourced in Haiti and the United States, together with aggregates sourced in the U.S. As illustrated in Table 1, compressive strengths of 2-in × 2-in (50.8 mm × 50.8 mm) cubes obtained using Haitian cements were 42 to 58 percent of those obtained with a U.S. cement for otherwise identical mix designs. The 28-day strengths were obtained for a water/cement ratio of 1.4 and approximate quantities by weight of cement (1), water (1.4), coarse aggregate (3), and sand (9). Reasons for the noticeable disparity in comparison with U.S. cements are being investigated. Given the apparent difference in cement quality and the reduced strengths obtained using recycled Haitian concrete as aggregate, mix designs should be finalized using locally sourced constituents.

2.3. Mechanical properties of Guadua Angustifolia

The structural system utilizes 3 to 4 in. (75 to 100 mm) diameter culms of Guadua Angustifolia. Because the forces in the bamboo frames are limited by the strength of the rebar dowel, the culms have ample strength. Reported strengths of Guadua Angustifolia vary with age at harvest and the height at which a sample was removed from the culm. For reference, ranges for mechanical properties of Guadua Angustifolia reported by others are summarized in Table 2, (11), (12), (13), (14).

2.4. Bamboo to CMU connection - dowel configuration

Figure 3 details the rebar dowel used at the base of each culm at the connection to the masonry plinth. Using the principles of capacity design, the rebar dowel is the ductile weak link in the system, conferring ductility to the system while limiting the forces that develop within the bamboo braced frame and its connections. Dowels having exposed lengths of 2- to 3-in. (50- to 75-mm) are considered to be the most practical to build with. Subsequent sections address the number of No. 3 (9.5-mm diameter) dowels of varied lengths that are required to resist seismic and wind loads for the prototype building.

Construction is achieved using a single No. 3 rebar fabricated with a sharp 90-degree hook with 1-in. (25-mm) extension. Once the frame is installed over the No. 3 rebar, the lowest two intermodal spaces of the culm are filled with mortar to anchor the bar. Laboratory tests indicated rebar embedment into a single internode space within the culm provided adequate strength. However, the diagonal brace frames into the first internode space, and to avoid potential detailing conflicts the brace connection, the vertical No. 3 bar is extended into the second internode space, as shown in Figure 3.

Figure 3. Rebar dowel connection at top of plinth wall.

2.5. Dowel behavior

Experimental and analytical results (20) led to the following recommendations for future work:

1. Although the mortar is able to adequately support the steel rebar when it develops plastic hinges, local crushing of the mortar can occur. A high-strength mortar or fiber reinforced mortar may avoid crushing and hence prevent migration of the rebar plastic hinges. Alternatively, annular inserts made of steel or other materials may be used to reduce bearing stresses between the rebar and mortar and reliably define the dowel’s effective length.
2. The effective length of dowel should not exceed perhaps 8Ø, which corresponds to 3 in. (75 mm) for No. 3 (9.5 mm) bars.
3. No. 3 (9.5-mm diameter) rebar could be assumed to have yield strength of 43 ksi (296 MPa), and resist a shear of 378 and 252 pounds (1.68 and 1.12 kN) upon plastic hinging at the ends of the 2- and 3-in. (50- and 75-mm) effective dowel lengths, respectively.
4. The effective yield displacements of the dowel are 0.009 and 0.020 in. (0.229 and 0.508 mm) for effective lengths of 2 and 3 in. (50 and 75 mm), respectively.
5. Axial load in the rebar dowel during seismic loading should be limited to 0.40Py = 0.40(43 ksi) (0.20 in²) = 3.44 kips (15.3 kN).

3.1. Braced frame configuration and seismic reactive weight

The proposed structure (Figure 4) illustrates braced frame configurations and dimensions needed to establish dead loads for use in seismic design. The rebar dowel carries the dead load tributary to each vertical culm, along with any overturning axial forces associated with the lateral load.

Figure 4. Prototype structural configuration.

Roof dead load was determined to be 2280 lbs (10.14 kN) based on bamboo (1.5 plf or 236 N/m), 1x4 wood purlins at 8 in. (200 mm) centers, galvanized sheet metal roofing (0.625 psf or 30 N/m²), 1” thick plaster on the gables (85 psf or 4070 N/m²), and rebar and wire averaging 0.25 psf (12 N/m²). Wall loads used the same material weights plus 20 lbs (0.09 kN) per mortared bamboo connection for a total structural weight to the frame bases of W = 9500 lbs (42.3 kN).

3.2. Inelastic spectra

The structural system is relatively light in comparison to the concrete and masonry structures typical of Haiti. Consequently, both wind and seismic loading demands were determined with details provided to ensure adequate ductility capacity for seismic loading. Since seismic design is more complex, it is addressed first.

To provide for a nearly universal design for varied site conditions, site specific spectra were established for Site Class D soils on the basis of the USGS Open File Report for Haiti (15). Using standard NEHRP notation, this report provides S_S = 1.64 g, S₁ = 0.61 g, F_a = 1.0, and F_v = 1.5, resulting in design spectral values of S_DS = (2/3) (1.64 g) (1.0) = 1.09 g and S_D1 = (2/3) (0.61 g) (1.5) = 0.61 g.

Inelastic spectra in the form of Yield Point Spectra are plotted in Figure 5. Curves of constant ductility, µ, (estimated using the R-C₁-T relationship of FEMA 440 (16) are plotted against the axes of yield strength coefficient, C_y, and system yield displacement (∆_{system_yield}). Thus, using a single-degree-of-freedom (SDOF) system to represent the response of the prototype building, the required strength to limit ductility (and hence, displacement) demands can be established for any estimated yield displacement.

Figure 5. Portion of Yield Point Spectra (Aschheim and Black, 2000) showing yield strength coefficients associated with different ductility demands (19).

3.3. System displacements

The required strength to limit system ductility (and hence peak displacement) is plotted as a function of yield displacement in Figure 5. The roof displacement associated with flexural deformation of the rebar dowel restrained from end rotation is estimated in Tables 3 and 4. In addition, the other structural components members are assumed to undergo elastic deformation. This deformation is assumed to consist of elastic deformation within the bamboo framing members and deformation at the bamboo frame connections. Thus, at effective yield of the system,

where ∆_{dowel_effective_yeild} = effective yield displacement of the rebar element, ∆_{bamboo_deformation} = the contribution of deformations within the bamboo framing members to the roof displacement, and ∆_slip = the contribution of connection slip to roof displacement at the effective yield level load.

Framing member deformations associated with axial loads are very small, while slip at the connection depends heavily on the connection details employed. The sensitivity of the design to connection slip was investigated, assuming connection slip contributes 0.05, 0.25, or 0.5 inches (1.27, 6.35, or 12.7 mm) of lateral displacement at the roof level.

Determination of the ductility demand that can be sustained by the structure depends on the contribution of the capacity-protected members to roof displacement. Since the system displacement results from inelastic demand concentrated within the rebar dowel, the allowable system ductility depends on the displacement that can be tolerated by the rebar dowel. Because the large inherent ductility of the steel comprising the rebar dowel, the displacement limit for the dowel was derived by imposition of limits associated with P-Delta effects.

Caltrans and AASHTO limits on P-Delta effects were considered in establishing the amount of deformation sustained by the rebar dowel. The proposed frame, as detailed in Figure 4, was analyzed at the effective yield strength corresponding to plastification of the rebar dowel to determine the associated overturning axial compression in the rebar dowel, P_OT. Tributary dead loads were considered to establish the gravity load contribution to the dowel axial force, P_gravity. Thus, the governing axial load to determine the limiting displacement of the dowel (∆_{limit_P-Delta}) considering P-Delta effects on a local member (rebar dowel) basis is given by P_govern = P_OT + P_gravity.

Analytic investigations as described in Section IV, show the rebar dowel, having length not exceeding perhaps 8F, can withstand large displacements without negative post yield effects for . However, to establish a displacement limit, existing limits applicable to bridge construction were applied. AASHTO limits the ratio P×D/M_p to not exceed 0.25, while Caltrans Seismic Design Criteria (18) limits the ratio P×D/M_p.to not exceed 0.20. These limits are applicable to cantilever columns. To explore the sensitivity of the design to this parameter, the AASHTO limit of 0.25 was used together with a more stringent value of 0.10. For the case of the rebar dowel, modeled as fixed at one end and guided to prevent rotation at the other, the lateral displacement at the top of the rebar dowel, D_lim-P-Delta, would be limited to

since V_yield = 2M_p/L.

The resulting displacement limit for the system is given by

The most restrictive P-Delta limit is obtained for the highest axial force. The culm with the largest dead load is considered together with superimposed overturning compression arising from the braced frame resisting lateral loads. The largest tributary weight on a dowel is represented by the weight tributary to any of the columns along the long perimeter wall, away from the corners. The tributary dead load, W, for this column was calculated to be 515 lbs. (2.29 kN). Additional overturning axial forces are also present. Thus, P_govern is taken equal to 1083 lbs (4.82 kN) and 894 lbs (3.98 kN) for 2 and 3-in. (50- and 75-mm) dowel lengths, respectively.

Thus, the limiting system ductility is given by

The above displacement limits and corresponding system ductility limits for rebar dowels of different clear lengths are quantified in Tables 3 and 4.

3.4. Dowels Required for Seismic Resistance

Using the inelastic spectra plotted in Figure 5, minimum yield strength coefficients (C_y) sufficient to limit system ductility to the values of Tables 3 and 4 were determined. Based on the required shear strength at yield, given by V_y = C_yW, the required number of rebar dowel connections (n) of a given clear length were determined. Key results are provided in Tables 3 and 4, for the AASHTO P-Delta limit of 0.25 and for the more restrictive value of 0.10.

A greater number of yielding dowel segments are needed when P-Delta requirements are satisfied using the more stringent ratio of 0.10. Since a long, slender culm is unlikely to cause yielding of a rebar dowel segment, the number of yielding dowel segments refers to those that are mobilized by an adjacent diagonal brace or bottom chord.

As Tables 3 and 4 display, 8 to 38 yielding rebar dowels are required for resisting seismic loading in each orthogonal direction of the building, depending on the effective length and P-Delta criterion used. The physical realization of the required number of rebar dowels may require additional diagonally braced bays.