Joint Rotational Stiffness Research Articles

Analysis of the steel frames with the semi-rigid beam-to-beam and beam-to-column knee joints under bending and axial forces

This paper presents an analysis of framework structures with semi-rigid joints. The semi-rigid end-plate bolted joints are subjected to bending and tension or a compression axial force. Usually the influence of an axial force on joint rotational stiffness is neglected. In some cases, the level of axial forces in the joints of structures can be significant and has a profound influence on characteristics of semi-rigid joints. One of the most popular practical methods permitting the determination of rotational stiffness and moment resistance of a joint is the so-called component method. The extension of the component method for evaluating the influence of bending moment and axial force on the rotational stiffness and moment resistance of a joint and an application to the analysis of framework structures are presented in the paper. The numerical results of calculations of steel frameworks are presented in this paper as well. The study shows that the estimation of axial force influence to rotation stiffness characteristics of the joint has significant influence on the distribution of internal forces and displacements of steel framework.

Abdominal Muscles Dominate Contributions to Vertebral Joint Stiffness during the Push-up

The goal of this study was to quantify the relative contributions of each muscle group surrounding the spine to vertebral joint rotational stiffness (VJRS) during the push-up exercise. Upper-body kinematics, three-dimensional hand forces and lumbar spine postures, and 14 channels (bilaterally from rectus abdominis, external oblique, internal oblique, latissimus dorsi, thoracic erector spinae, lumbar erector spinae, and multifidus) of trunk electromyographic (EMG) activity were collected from 11 males and used as inputs to a biomechanical model that determined the individual contributions of 10 muscle groups surrounding the lumbar spine to VJRS at five lumbar vertebral joints (L1-L2 to L5-S1). On average, the abdominal muscles contributed 64.32 +/- 8.50%, 86.55 +/- 1.13%, and 83.84 +/- 1.95% to VJRS about the flexion/extension, lateral bend, and axial twist axes, respectively. Rectus abdominis contributed 43.16 +/- 3.44% to VJRS about the flexion/extension axis at each lumbar joint, and external oblique and internal oblique, respectively contributed 52.61 +/- 7.73% and 62.13 +/- 8.71% to VJRS about the lateral bend and axial twist axes, respectively, at all lumbar joints with the exception of L5-S1. Owing to changes in moment arm length, the external oblique and internal oblique, respectively contributed 55.89% and 50.01% to VJRS about the axial twist and lateral bend axes at L5-S1. Transversus abdominis, multifidus, and the spine extensors contributed minimally to VJRS during the push-up exercise. The push-up challenges the abdominal musculature to maintain VJRS. The orientation of the abdominal muscles suggests that each muscle primarily controls the rotational stiffness about a single axis.

Exploring the geometric and mechanical characteristics of the spine musculature to provide rotational stiffness to two spine joints in the neutral posture

Joint stiffness is inherently linked to both performance and injury. Muscular activation is the predominant provider of stiffness to the lumbar spine, and is essential to ensure optimal spine performance. The purpose of the current paper was to examine the potential of the trunk muscles to provide rotational joint stiffness at two spine joints in the neutral posture, and to demonstrate the sensitivity of this stiffening potential to various muscle orientation and stiffness assumptions. Two separate anatomical models were utilized to analyze the muscular contributions to the 3-dimensional rotational stiffness about each of the L1–L2 and L4–L5 spine joints. Total muscular stiffening potentials, for both joints in each anatomical model, were found to be highest about the global lateral bend axis, and lowest about the global axial twist axis. The stiffening potential was found to depend highly on both the assumed muscle stiffness coefficient (q value) and the moment arm of the muscle about the joint in question. Analyses of spine stiffness were found to be greatly affected by both the anatomical representation of the surrounding musculature and the selection of the q value in the determination of muscular stiffness. Inappropriate choices of either of these factors could lead to errors in stiffness and subsequently stability estimates, and in the interpretation and possible clinical recommendations stemming from such estimates.

Development of a closed-form 3-D RBS beam finite element and associated case studies

The 1994 Northridge and the 1995 Kobe earthquakes demonstrated that steel moment resisting frames (SMRF) which were traditionally considered to provide an ideal structural system in resisting lateral earthquake loads could indeed suffer brittle fractures at the beam–column connections. To remedy this, competing connection design improvements have been adopted, among which is the radius-cut Reduced Beam Section (RBS) moment connection. As the design of a vast majority of these SMRF buildings is drift-controlled, the reduction in lateral stiffness and hence the increase in drifts in general 3-dimensional SMRF buildings with RBS moment connections–particularly those with torsional irregularity–is investigated here through development and verification of a new closed-form 3-D RBS finite element based on Timoshenko’s shear deformation theory for beams. The study shows that the increase in story drifts in 3-dimensional torsionally irregular SMRF buildings with RBS moment connections could be as high as 15% under the action of lateral and gravity loads. This is in contrast to the current recommendation of increasing elastic story drifts by a maximum of 9%–10% for SMRF buildings to account for stiffness reduction in the presence of RBS connections. The study also shows that the decrease in weak axis joint rotational and shear stiffness coefficients of beams with RBS connections on both sides–and unsupported laterally–could be as high as 67% for flange area reductions of only 30%.

Behaviour of end-plate moment connections under earthquake loading

A series of eight full-scale structural steel beam-to-column end-plate moment connection specimens was tested under cyclic loads. The parameters investigated were end-plate thickness, bolt diameter, end-plate extended stiffener, column stiffener, type of flush and extended end-plate. The experimental results are presented in terms of moment capacity, rotational stiffness, rotation capacity and hysteretic curves. The test results indicate that extended end-plate connections have adequate strength, joint rotational stiffness, ductility and energy dissipation capacity required for use in seismic moment frames. Based on the test results and analysis, details on end-plate moment connections for seismic steel frames has been proposed, three failure mode requirements and the corresponding resistance have been recommended to assure that the end-plate connection can provide enough rotation capacity and energy dissipation capacity under earthquake loading and its ultimate failure mode is ductile. A bilinear kinematic hardening hysteretic moment–rotation (M–ϕ) model for the end-plate connection extended on both sides has been proposed.

Behaviour of semi-rigid steel beam-to-beam joints under bending and axial forces

This paper presents an analysis of semi-rigid beam-to-beam end-plate bolted joints that are subjected to bending and tension or a compression axial force. Usually the influence of axial force on joint rotational stiffness is neglected. According to EC3, the axial load, which is less than 10% of plastic resistance of the connected member under axial force, may be disregarded in the calculation of characteristics of a joint. Actually, the level of axial forces in joints of structures can be significant and has a significant influence on characteristics of semi-rigid joints. One of the most popular practical methods permitting the determination of rotational stiffness and moment resistance of a joint is the so-called component method. The extension of the component method for evaluating the influence of bending moment and axial force on the rotational stiffness and moment resistance of a joint are presented in the paper. The numerical results of calculations of characteristics of joints and calculations of steel framework are presented in this paper as well.

Increased musculoskeletal stiffness during load carriage at increasing walking speeds maintains constant vertical excursion of the body center of mass

The primary objective of this research was to determine changes in body and joint stiffness parameters and kinematics of the knee and body center of mass (COM), that result from wearing a backpack (BP) with a 40% body weight load at increasing speeds of walking. It was hypothesized that there would be speed and load-related increases in stiffness that would prevent significant deviations in the COM trajectory and in lower-extremity joint angles. Three independent biomechanical models employing kinematic data were used to estimate global lower-extremity stiffness, vertical stiffness and knee joint rotational stiffness in the sagittal plane during walking on a treadmill at speeds of 0.6–1.6 m s −1 in 0.2 m s −1 increments in BP and no backpack conditions. Kinematic data were collected using an Optotrak, three-dimensional motion analysis system. Knee angles and vertical excursion of the COM during the compression (loading phase) increased as a function of speed but not load. All three estimates of stiffness showed significant increases as a function of both speed and load. Significant interaction effects indicated a convergence of load-related stiffness values at lower speeds. Results suggested that increases in muscle-mediated stiffness are used to maintain a constant vertical excursion of the COM under load across the speeds tested, and thereby limit increases in metabolic cost that would occur if the COM would travel through greater vertical range of motion.

Plywood frame corner joints with glued-in hardwood dowels

This paper presents research on plywood frame corners jointed to glulam beams and columns by means of glued-in hardwood dowels. The frame corner was made of a solid block of ordinary plywood of the same width as the glulam beams and with plies parallel to the plane of the frame to avoid splitting due to stress perpendicular to the grain. Hardwood dowels with a diameter of 12mm and a maximum glued-in length of 120mm were glued into drilled holes in the plywood corner and glulam beam ends parallel to the grain direction of the beams to form a momentresisting joint. Static bending tests were conducted of frame corners with 100 X 200mm2 and 120 X 420mm2 beam cross sections. Bending capacities of the joints corresponding to a modulus of rupture of the jointed glulam beams of about 30MPa were obtained for both closing and opening moments for the small cross sections, and about 22MPa was obtained for the large cross sections. Simple design models for calculation of joint strength and rotational stiffness are also presented.

Practical design guidlines for semi-continuous composite braced frames

This paper presents a simplified approach for the design of semi-continuous composite beams in braced frames, where specific attention is given to the effect of joint rotational stiffness. A simple composite beam model is proposed incorporating the effects of semi-rigid end connections and the nonprismatic properties of a `cracked` steel-concrete beam. This beam model is extended to a sub-frame in which the restraining effects from the adjoining members are considered. Parametric studies are performed on several sub-frame models and the results are used to show that it is possible to correlate the amount of moment redistribution of semi-continuous beam within the sub-frame using an equivalent stiffness of the connection. Deflection equations are derived for semi-continuous composite beams subjected to various loading and parametric studies on beam vibrations are conducted. The proposed method may be applied using a simple computer or spreadsheet program.

Practical design guidlines for semi-continuous composite braced frames

This paper presents a simplified approach for the design of semi-continuous composite beams in braced frames, where specific attention is given to the effect of joint rotational stiffness. A simple composite beam model is proposed incorporating the effects of semi-rigid end connections and the nonprismatic properties of a 'cracked' steel-concrete beam. This beam model is extended to a sub-frame in which the restraining effects from the adjoining members are considered. Parametric studies are performed on several sub-frame models and the results are used to show that it is possible to correlate the amount of moment redistribution of semi-continuous beam within the sub-frame using an equivalent stiffness of the connection. Deflection equations are derived for semi-continuous composite beams subjected to various loading and parametric studies on beam vibrations are conducted. The proposed method may be applied using a simple computer or spreadsheet program.

Member capacity of columns with semi-rigid end conditions in Oktalok space frames

The Oktalok nodal connection system is an aesthetic and efficient system. It has been widely used throughout Australia. The paper will briefly introduce the concept and application of the Oktalok nodal system. The existing design method is based on the assumption that the joints are pin-ended, i.e., the rotational stiffness of the joints is zero. However the ultimate capacity of the frame may increase significantly depending on the rotational stiffness of the joints. Stiffness tests and finite element simulations were carried out to determine the rotational stiffness of the Oktalok joints. Column buckling tests and non-linear finite element analyses were performed to determine the member capacity of columns with semi-rigid end conditions. A simple formulae for the effective length factor of column buckling is derived based on the above experimental and theoretical investigations.

Electrical stimulation for the treatment of spasticity in cerebral palsy

Knee valgus during landing has been identified as a strong correlate of ACL injury. Inappropriate trunk control during landing contributes to high knee valgus, with neuromuscular factors related to core stability postulated as the mechanism. This investigation probed the influence of trunk and hip mechanics, including joint stiffness, on knee mechanics, particularly high knee valgus. Specifically, this study quantified lumbar spine and hip joint rotational stiffness (a proxy for mechanical joint stability) during single-leg landing tasks known to be associated with injury risk, particularly in females. Kinematics, kinetics, and 24 channels of electromyography spanning the trunk and hip musculature were measured in 18 healthy female participants. Anatomically detailed EMG-driven musculoskeletal models quantified lumbar spine and hip joint rotational stiffness. The links between peak knee abduction angle and moment with lumbar spine and hip joint rotational stiffness were measured. Hip joint rotational stiffness influenced knee abduction across tasks (correlation coefficient ranging from −0.48 to −0.70, p < 0.05) to reduce valgus deviation. Similarly, transverse plane hip joint rotational stiffness during landings reduced knee abduction moment (R = -0.50, P = 0.03; R = -0.49, P = 0.04), and lumbar spine joint rotational stiffness reduced knee abduction angle and moment but did not consistently reach statistical significance. The control system uses stiffness to control motion. This study demonstrates the importance of proximal (lumbar spine and hip) joint rotational stiffness (i.e. core control stability) during single-leg landing to prevent knee abduction motion. Instantaneous core stability is achieved with the coordinated activation and stiffness of both trunk and hip muscles.

A numerical approach to define the rotational stiffness of a prefabricated connection and experimental study

A numerical approach is proposed to define the elastic rotational stiffness of a typical joint on the top beam of a prefabricated reinforced concrete gable frame structure. The 12 degrees of freedom triangular plane stress finite element is used to examine the connection region. Using this joint rotational stiffness value, realistic results are obtained in the frame analysis. The experimental verification is performed by means of the photoelastic method. Following the proposed method, an effective joint length with reduced moment of inertia is defined and using this concept the frame solution is simply achieved, including the existence of joint.

Quantification of dynamic rotational joint stiffness to identify patients with loose prosthetic femoral stems

Quantification of dynamic rotational joint stiffness to identify patients with loose prosthetic femoral stems

Effect of Posttensioning on Rotational Stiffness of Wood Joints

The moment-rotation behavior of full-size Warren truss timber connections, using posttensioning as a possible reinforcement scheme, was investigated and compared with the current method of using gusset plates. Four joint configurations were tested using three posttensioning levels. The stiffness of the joints was calculated and is presented in this technical note. Based on the results of posttensioned joints and earlier experimental investigations, it was found that the increase in joint rotational stiffness, due to transverse posttensioning is a function of the number of connector rods in the joint zone for both inner (compression) and outer (tension) web members, and the increase in joint rotational stiffness due to transverse posttensioning is a function of the posttension level for outer (tension) web members.

Theoretical analysis of haunch-reinforced T-joints in square hollow sections

A theoretical analysis has been undertaken for unequal width T-joints, haunch-reinforced, in square hollow structural sections (HSS). The unreinforced joint is merely a special case. The theory was based on a finite difference solution to the elastic chord flange plate equation and predicts the branch-to-chord joint stiffnesses under both bending [Formula: see text] and axial force (C = P/δ). The effects of varying the width ratio λ, overall haunch length-to-width ratio λ1, and chord width-to-thickness ratio bc/tc were studied for different plate edge boundary conditions. The latter parameter has the greatest effect on stiffness, but the other two, including haunch size, are also significant. There is reasonable agreement between the joint rotational stiffness factor J, obtained from earlier tests, and the predictions of theory for different edge boundary conditions. The unequal width, unreinforced connection is generally too weak to be viable in design applications. Haunch stiffeners improve strength and stiffness, and are particularly beneficial for large rather than small λ (i.e., 0.833 vs. 0.333).