Truss Action Research Articles

A truss-arch model-based method for calculating shear walls with small shear span ratio

In this paper, based on the equivalent diagonal web truss-arch (EDWT) model and considering different failure modes and deformation coordination conditions, a method for calculating the shear capacity of shear walls with small shear-to-span ratio is proposed. The method considers the effects of both horizontal and vertical reinforcements in the web on the shear capacity of the member through the stress equivalence principle in the truss action, and an empirical formula to calculate the height of the compression zone for determining the section height of the concrete diagonal compression truss are also proposed. The test data of 359 small shear-span ratio shear walls were collected, and their shear capacity was calculated using the method proposed in this paper, and compared with the Chinese, American, European and Japanese codes. The results show that: except for the Japanese AIJ code, the calculation of shear capacity of small shear span ratio shear wall is conservative, while the AIJ code overestimates the height of the arch bar, which makes its calculation results unconservative; while the proposed formula can calculate the shear bearing capacity of small shear span ratio shear wall more accurately.

Simplified evaluation of the shear strength of slender rectangular R.C. members with shear reinforcement

This paper describes a simple analytical tool for the calculation of the shear strength of R.C. rectangular members with shear reinforcement and subjected to only truss action. The proposed method considers simplified stress fields and evaluates the shear strength of members subjected to axial force, bending moment and shear force by means of the application of the static theorem of limit analysis. The proposed method considers a single physical model to explain the resistance to axial force, bending moment and shear force, and simultaneously satisfies the equilibrium under all the above internal forces. The paper identifies basic points of the N-M-V ultimate domain and reports relations and procedures to calculate the values of the internal forces of these points as well as the internal forces of the points in between. The method is applied to a set of beam and column members and a comparison is drawn between the shear strength resulting from the simplified method and that from a more complex non-linear mathematical program proposed in the past by one of the authors. Finally, the proposed method is applied to members tested in laboratory by other researchers and characterized by different geometric and mechanical properties.

Shear behavior of UHPC beams with small shear span to depth ratios based on MSTM

Ultra-high performance concrete (UHPC) has been gradually used in structural engineering due to its excellent mechanical performance, however, predicting the shear behavior of the UHPC beams at service load conditions is still a big challenge, especially for the beams with small shear span to depth ratio. To address this issue, this paper devotes to develop a modified strut and tie model (MSTM) to predict the shear behavior of the UHPC beams with stirrups throughout the loading process. The principle of stationary complementary energy has been introduced into the MSTM to decouple the contribution of arch action and truss action on shear forces. Based on the MSTM, the shear force resistance mechanism has been revealed, and simplified models at each load step have been developed to estimate the shear behavior of UHPC beams. 12 UHPC beams were designed and tested to validate the proposed model. The proposed model was verified to be sufficiently accurate. Moreover, it can be noted that the current design codes, including SETRA-AFGC and SIA, give overly conservative values for UHPC beams when the shear span to depth ratio is less than 2.5.

Numerical study on the flexural behaviour of normal- and high-strength concrete beams reinforced with GFRP bar, using different amounts of transverse reinforcement

This study was numerically focused on the non-linear behaviour of glass fibre reinforced polymer (GFRP) reinforced concrete beams with different amounts of transverse reinforcement. The mid-span deflection of concrete beam cannot effectively be restricted using higher amount of flexural GFRP bars, owing to their low deformability factor. So, the use of high transverse reinforcement ratio is proposed to decrease the mid-span deflection and crack widths. Following this, the effect of reinforcement is required to carefully assess to better understand the flexural behaviour of concrete beams. The main goal of this study was to numerically evaluate the mid-span deflection, stress distribution and failure mechanism of normal- and high-strength concrete beams with low and high flexural reinforcement ratios (GFRP bar) and different amounts of transverse reinforcement using finite element (FE) analysis. The results revealed a fair agreement between the developed FE models and experimental beams. Besides, the mean value of experimental-to-predicted load ratio was 0.96, with average coefficient of variation of 2.69 %. Moreover, the truss action mechanism generated the diagonal compression in the cracked concrete and tension in the transverse reinforcement, resulted in decreasing the mid-span deflection. In addition, for all specimens with and without transverse reinforcement, the highest stress intensities were observed in the bottom of concrete component at service load. However, by increasing the load from service to ultimate, the use of transverse reinforcement caused to propagate some parts of high stress intensities near to the sides of concrete component. Furthermore, the presence of the transverse reinforcement resulted in distributing the stress intensity in the normal-strength concrete beams more than that in the high-strength concrete beams either at service load or at ultimate load.

RESEARCH INTO THE DEVELOPMENT OF A RESPONSE MODIFICATION FACTOR FOR DIAGRID STRUCTURES

The diagrid structure system has recently gained popularity as an effective structural system for high rise buildings. The effectiveness of the system relies on the truss action developed by the perimeter diagrid system to resist lateral loads. In active seismic zones, ductile performance of the lateral resisting system is highly desired to dissipate energy developed in the structure from the ground shaking. In this study, the seismic performance of the diagrid system is investigated. Non-linear static pushover analysis followed by non-linear dynamic analysis were conducted to study the inelastic behaviour of diagrid systems. Through methods of analysis, the response modification factor of the modelled system was calculated. The results indicate that the reserve strength of a diagrid system is comparable to and often greater than that of many other lateral structure systems, such as steel special truss moment resisting frames and other structural systems as prescribed by the ASCE 7-10.

Decoupling of arch action and truss action in deep beams by strain energy

It is commonly accepted that deep beams transfer shear forces through a combination of arch action and truss action, but there is disagreement on how to estimate the fraction transferred by each assumed action. This study provides a theoretical method to decouple the two shear-carrying mechanisms from the perspective of strain energy. Through multiple-level least-energy solutions, a two-panel truss consisted of parallel compression diagonals and orthogonal tension ties is obtained for the minimum strain energy. Assuming that vertical ties of the truss model and diagonal ties of the combined model have the same energy, the fraction of load transferred by the truss action is decoupled as 2λ/3–0.5 (where λ is the shear span-depth ratio). It means that the entire shear is carried by the arch action when λ ≤ 0.75, while the entire shear is carried by the truss action when λ ≥ 2.25. Six deep beams were tested with instruments placed along the assumed direct struts and indirect struts, from which the contributions of the two load-transfer mechanisms can be separated experimentally. The theoretical method agrees well with the experimental results of the current study and the others collected from the literature.

Influence of horizontal restraints on the behaviour of vertical disproportionate collapse of RC moment frames

Current research studies on progressive collapse of reinforced concrete (RC) moment frames mainly focus on the RC frames with strong horizontal restraints in which collapse only propagates in the vertical direction. Notwithstanding, progressive collapse may propagate in the horizontal direction due to insufficient lateral stiffness and bearing capacity of the real-world structural systems, eventually triggering a wider range of damage associated with a disproportionate collapse. A static collapse test on three asymmetric beam-column substructure specimens with flange slabs was conducted to analyse the effects of different lateral restraints on the progressive collapse behaviour of RC beam-column specimens. The three specimens, including two one-story and one two-story substructures, are designated as OP, TP and OA, in which OP and OA represent one-story penultimate and antepenult column removal scenarios, respectively, while TP represents a two-story penultimate column removal scenario. Comparing to OP, an extra bay and an extra floor were added in OA and TP, respectively, to create different horizontal restraint scenarios. Experimental results show that under the compressive arch action (CAA), the contribution of the CAA within the beams and slabs in OP and TP was significantly reduced compared to that in OA. Under the catenary action (CA), the collapse resistance of OA was found to develop rapidly to exceed even the peak resistance of CAA, whereas the resistance of OP and TP varied marginally, caused by the continuously released axial force of rebars within the beams and flange slabs. Additionally, the final failure mode of all three specimens demonstrated a compression-bending failure of the edge and penultimate columns. Subsequent to the experiments, a fibre-beam-element-based model was built to analyse the development of the internal forces within the slab-flange beams and columns. In the numerical analyses, the penultimate column in OA was found to damage prior to the edge column, owing to its larger axial force generated from the redistributed force and the additional bending moment. While in TP, the so-called Vierendeel truss action led to an uneven internal force distribution developed within the two floors, causing the failure to propagate from the lower story to the upper story. Finally, design recommendations are provided based on the results obtained from the experimental test and numerical simulation.

Theoretical and experimental study on shear strength of precast steel reinforced concrete beam

With the aim to put forward the analytical model for calculating the shear capacity of precast steel reinforced concrete (PSRC) beams, a static test on two full-scale PSRC specimens was conducted under four-point loading, and the failure modes and strain developments of the specimens were critically investigated. Based on the test results, a modified truss-arch model was proposed to analyze the shear mechanisms of PSRC and cast-in-place SRC beams. In the proposed model, the overall shear capacity of PSRC and cast-in-place SRC beams can be obtained by combining the shear capacity of encased steel shape with web concrete determined by modified Nakamura and Narita model and the shear capacity of reinforced concrete part determined by compatible truss-arch model which can consider both the contributions of concrete and stirrups to shear capacity in the truss action as well as the contribution of arch action through compatibility of deformation. Finally, the proposed model is compared with other models from JGJ 138 and AISC 360 using the available SRC beam test data consisting of 75 shear-critical PSRC and SRC beams. The results indicate that the proposed model can improve the accuracy of shear capacity predictions for shear-critical PSRC and cast-in-place SRC beams, and relatively conservative results can be obtained by the models from JGJ 138 and AISC 360.

Evaluation of earthquake load resistance of masonry infilled RC frames using linear and non-linear dynamic analysis

The understanding of the dynamic behavior of structures is essential to design them to resist the lateral loads due to earthquakes. Recent past earthquakes have demonstrated the importance of proper designing of structural members to avoid damages in the buildings and loss of life. Generally the lateral load resistance of masonry infilled moment resisting frames is achieved by frame action and truss action. In this paper the seismic performance of a G + 9 storeyed masonry infilled RC framed building is evaluated by linear and non-linear dynamic analysis. The analysis is carried out using the finite element software-ETABS. The response spectrum and time history pertaining to the specifications as given in the Indian Seismic Code IS 1893:2016 is considered for the analysis. Three different frame models are studied namely, bare frame, fully infilled frame and soft storey frame to understand the lateral load resistance of the frames. The dynamic characteristics of the frames such as time period, frequency, mode shapes, storey displacements, inter-storey drift, over-turning moments and energy dissipation capacity are evaluated and compared. The fully infilled frame shows better seismic behavior than that of other two frames though it attracts more forces.

Shear Transfer in Normal- and High-Strength Recycled Aggregate Concrete

AbstractShear strength of interfaces in virgin aggregate and in recycled aggregate concrete has been investigated using initially uncracked pushoff specimens by varying the following parameters: replacement level of the recycled aggregates (0 %, 50 %, and 100 %), concrete grade (normal strength and high strength) and the clamping force on the shear plane. The experimentally observed crack patterns in the pushoff specimens were indicative of the development of truss action for resisting interface shear. A truss-based analysis recommended in the literature, in combination with a simplified failure envelope for concrete subjected to biaxial stresses, has been used for shear-strength prediction of both the concrete types. The proposed methodology has been calibrated, with the help of the experimental results, to obtain a nominal distribution of shear stresses across the slip plane and conservative and reasonably accurate shear-strength predictions were noted for the selected experimental results taken from the literature.

Shear strength of interfaces in natural and in recycled aggregate concrete

Shear strength of interfaces in natural aggregate concrete and in recycled aggregate concrete has been investigated using initially uncracked push-off specimens by varying the following parameters: replacement level of the recycled aggregates (0%, 50%, and 100%), concrete grade (normal-strength and medium-strength), and clamping force on the shear plane. Development of truss action for resisting interface shear was indicated by the observed crack patterns in the tested specimens and a truss-based analysis recommended in the literature in combination with a simplified failure envelope for concrete subjected to biaxial stresses has been used for shear strength predictions of the tested specimens. The proposed methodology, which is considered to be more rational than the empirical shear strength models available in the literature was calibrated for both the concrete types and gave conservative and reasonably accurate shear strength predictions for selected experiments taken from the literature.

Effect of staircase on seismic performance of RC frame building

Staircase is a vertical transportation element commonly used in every multistoried structure. Inclined flights of staircase are usually casted monolithically with RC frame. The structural configuration of stairs generally introduces discontinuities into the typical regular reinforced concrete frame composed of beams and columns. Inclined position of flight transfers both vertical as well as horizontal forces in the frame. Under lateral loading, staircase in a multistory RC frame building develops truss action creating a local stiffening effect. In case of seismic event the stiff area around staircase attracts larger force. Therefore, special attention is required while modeling and analyzing the building with staircase. However, in general design practice, designers usually ignore the staircase while modeling either due to ignorance or to avoid complexity. A numerical study has been conducted to examine the effect of ignoring staircase in modeling and design of RC frame buildings while they are really present in structure, may be at different locations. Linear dynamic analysis is performed on nine separate building models to evaluate influence of staircase on dynamic characteristics of building, followed by nonlinear static analysis on the same models to access their seismic performance. It is observed that effect of ignoring staircase in modeling is severe and leads to unsafe structure. Effect of location and orientation of staircase is also important in determining seismic performance of RC frame buildings.

Parameter Study of a New Strut-and-Tie Model for a Thick Cap with Six Piles

A comprehensive strut-and-tie model is a function of the nodes, struts, ties, model types, and pile reaction force. Because each element has more than one solution, the function is a problem of permutations and combinations. This paper presents a new strut-and-tie model that yields a satisfactory simulation result. In the model, a model type of truss action, direct arch action, or a combination of both actions was selected independently for the side and angle piles. The node and tie parameters were also modified. The pile reaction force distribution and the failure mechanism for inclined struts were also considered. However, because the authors’ previous study did not include a detailed analysis or an in-depth exploration, the effect of these critical factors is discussed in this paper at length. The model, which was programmed using the MATLAB language, was used to sequentially analyze the possible solutions for each member (nodes, ties, and struts). Different solutions for the ratio of truss action and direct arch action were also compared. The inclined struts with variable cross sections were tested under various failure mechanisms. Furthermore, the effect of the pile reaction force, which was distributed using model test measurements and theoretical (elastic or rigid) analyses, was analyzed. Comparison of the solutions indicated that the function f, which included the essential elements described above, was both rational and accurate.

Shear Strength Model for Reinforced Concrete Columns with Low Transverse Reinforcement Ratios

This paper introduces an equation developed based on the strut-and-tie analogy to predict the shear strength of reinforced concrete columns with low transverse reinforcement ratios. The validity and applicability of the proposed equation are evaluated by comparison with available experimental data. The proposed equation includes the contributions from concrete and transverse reinforcement through the truss action, and axial load through the strut action. A reinforced concrete column with a low transverse reinforcement ratio, commonly found in existing structures in Singapore and other parts of the world was tested to validate the assumptions made during the development of the proposed equation. The column specimen was tested to failure under the combination of a constant axial load of 0.30 f'cAgand quasi-static cyclic loadings to simulate earthquake actions. The analytical results revealed that the proposed equation is capable of predicting the shear strength of reinforced concrete columns with low transverse reinforcement ratios subjected to reversed cyclic loadings to a satisfactory level of accuracy

Sub-Paneling of Masonry Walls Using Precast Reinforced Concrete Elements for Earthquake Resistance

Some traditional designs of masonry structures have shown acceptable structural performance during past earthquakes. In these structures, a grid of horizontal, vertical, and/or diagonal elements divide a large wall into smaller wall areas and provide confinement to masonry panels. In addition, grid elements provide a definite shearing plane along which masonry blocks can slide adding to deformability and energy-dissipation capacity. Inclined elements significantly add to lateral stiffness and strength depending on whether they can develop a complete truss action for lateral loads. Cyclic tests were conducted on five half-scaled wall specimens with different sub-paneling schemes using RC precast grid elements. Experimental results and finite element studies were used to develop simplified predictive relations for strength and stiffness response based on a confinement factor representing the grid element density. These relations can be used to configure the grid elements for desired performance levels with additional inputs about the global behavior.

FORMULAE TO EVALUATE STRUCTURAL PERFORMANCE OF SHEATHED WALLS WITH UNCOVERED POSTS IN CONVENTIONAL POST AND BEAM STRUCTURES

Generally in Japanese style rooms, sheathed walls with uncovered post have widely been used instead of mud walls. The sheathing material is nailed and inserted in the frame with noggins. The formula to calculate the elastic strength, yield point, ultimate strength and the ductility factor has been derived for the sheathed wall, considering the elements of the shear resistance of the nail strucked in the noggins and frame, and the diagonal compression resistance of the sheathing material as truss action. In order to verify the formula, the shear racking tests of sheathed walls have been carried out where plywood and plasterboard have been used as sheathing materials. It is clear that the formula is sufficiently accurate to predict the elastic and plastic behavior of sheathed walls with uncovered post for structural calculation.

Non-bernoulli-compatibility truss model for RC members subjected to combined action of flexure and shear: Part I: Its derivation of theoretical concept

An enhanced truss model is presented in the present study. The model is theoretically based on the well-known relationship between shear and the rate of change of bending moment in a reinforced concrete beam subjected to combined shear and moment loads. The new model shows that a new perspective on the shear resistance can be gained by considering the variation of the internal arm length along the span. And the shear resistance mechanism is resolved into three independent base components; arch action, truss action and membrane action. The compatibility of deformation associated to the two actions is indirectly taken into account by employing an empirical factor. Then the base equation of V=dM/dx is numerically formulated so as to clarify the physical basis of the behavior related to beams under combined action of flexure and shear.

Out-of-Plane Shear Strength of Steel-Plate-Reinforced Concrete Walls Dependent on Bond Behavior

This paper investigates the out-of-plane shear behavior of composite steel-plate-reinforced concrete walls (SC walls) and proposes their shear-strength-models based on plasticity theory limit analysis. For speedy, modular construction, SC walls are fabricated using double-skin steel plates with welded shear studs and sandwiching concrete between them. A review of current design formulas provides better understanding of bond-stress-dependent shear behavior relying on studs of SC walls. We conducted experiments on bondstrength-dependent arch and/or truss action to verify proposed shear-strength models with test results. Test results, including those from literature, agreed well with the strength anticipated by proposed formulas.

Evaluation of Load Transfer and Strut Strength of Deep Beams with Short Longitudinal Bar Anchorages

This paper examines the behavior of struts and nodes in deep beams fabricated using short longitudinal bar anchorages. Laboratory tests were conducted of 12 deep beams in which the longitudinal reinforcement was anchored into the support using short straight bar anchorages. The shortest anchorage lengths provided were below 50% of those required by ACI 318-08 Chapter 12 provisions. Four different specimen groups were constructed using three different shear span-depth ratios (a/d) and two longitudinal bar sizes. Most of the beams failed by strut crushing after yielding of the main longitudinal reinforcement at midspan. Only those specimens with the shortest anchorage length in each group developed concrete splitting failures along the anchorage region. The effect of a/d and anchorage length on strut strength and load transfer mechanism observed in the tests is presented and discussed. Test results indicate that a significant portion of the applied shear force may be transferred through truss action even in beams with low a/d. Short anchorage length affected the load transfer characteristics of the deep beams. These findings can be used in better understanding the merits of different strut-and-tie models for design of deep beams.

FORMULAE TO PREDICT THE ELASTIC AND PLASTIC BEHAVIOR OF SHEATHED WALLS WITH UNCOVERED POSTS IN CONVENTIONAL POST AND BEAM STRUCTURES

Generally in Japanese style rooms, sheathed walls with uncovered post have spread instead of mud walls. The sheathing material is nailed and inserted in the frame with noggings. The formula to calculate the elastic strength, yield point, ultimate strength and the ductility of factor has been derived for sheathed wall, considering the elements of the shear resistance of the nail struck in the noggings and frame, and the diagonal compression resistance of the sheathing material as truss action. In order to verify the formula, the shear examinations of sheathed walls have been carried out where five kinds of different sheathing material have been used. It is clear that the formula is sufficiently accurate to predict the elastic and plastic behavior of sheathed walls with uncovered post for structural calculation.