Key words : oblique bending, internal compression-tension, strength conditions.
The type of deformation is complex when two or more force factors arise in the cross section of the rod. A complex type of deformation can be considered as the sum of simple types studied earlier (tension, bending, torsion), if the principle of independence of the action of forces is applied (a special case of the principle of superposition or imposition, used in the mechanics of a deformable solid).
Let us recall the formulation of the principle of independence of the action of forces: stress (strain) from a group of forces is equal to the sum of stresses (strains) from each force separately . It is valid if the function and the argument are related by a linear relationship. In problems of mechanics of materials and structures it becomes inapplicable if:
For example, the differential equation for the bending of a rod is nonlinear and the resulting dependence of the deflection f on the load P for the cantilever beam shown in Fig. 1, a, is also nonlinear (Fig. 1, b). However, if the beam deflections are small ( f< ) so that (dv/dz) 2 <<1 (since dv/dz
f/l ), then the differential bending equation becomes linear (as can be seen from Fig. 1, b, the initial section of the dependence of P on f , described by this equation, is also linear).
It is known that oblique bending occurs when the forces causing it do not lie in one of the main planes of inertia. However, if we expand the external forces along the main axes of inertia Ox and Oy , we obtain two systems of forces P 1x , P 2x , . , P nx and P 1y , P 2y , . , P ny , each of which causes direct bending with bending moments My and Mx, (Fig. 2). Applying the principle of independence of the action of forces, we define normal stresses s (Fig. 3) as the algebraic sum of stresses from M x and M y :
In order not to be bound by formal rules of signs, we will define the terms by their modulus and assign the signs according to their meaning. We define the deflections of the beam as the geometric sum of deflections due to straight bends (Fig. 2)
Thus, the calculation for oblique bending using the principle of independence of forces is reduced to the calculation for two straight bends with subsequent algebraic summation of stresses and geometric summation of deflections.
In the case of cross sections having two axes of symmetry and protruding corner points (Fig. 4) with equal modulus and maximum coordinates of the same name, the stresses at these points will be equal
It is recommended to determine the terms in this expression by modulus, and put the signs according to their meaning. For example, in Fig. 5, the upper row of signs “+” and “-” corresponds to voltages from M x , and the bottom row - from M y , and the voltages at these points will be equal
The strength condition for beams made of plastic material with the specified type of sections will be written in the form
In other cases, to determine max a (or max dp and max | s c | for a brittle material), it is necessary to check the stresses at all suspicious points using the general formula.
There is another way: putting s = 0, we obtain the equation of the neutral line. Since the stresses at the points of the cross section will be proportional to the distances from the neutral line, max s will occur at the points most distant from it.
Copyright © 2000-2006 Department of "CAD in Construction" MGSU All rights reserved.
Foot deformity is a permanent change in the natural appearance of the foot caused by a change in the shape or length of one or more bones, shortening of tendons or disorders of the ligamentous apparatus. Since the foot is a single functional formation, pathological processes in any part of it entail a restructuring of the remaining anatomical structures. Foot deformation leads to impaired support, changes in gait and redistribution of body weight. As a result, not only the joints, bones and ligaments of the distal parts of the limb are affected, but also the spine and large joints. Foot deformities can develop as a result of injuries, developmental defects and certain diseases. The diagnosis is made based on examination and the results of radiological studies (x-rays, MRI, CT). Treatment depends on the type of pathology and can be either conservative or surgical.
Foot deformities are a group of pathological conditions in which there is a change in the appearance of the foot. This group includes a variety of disorders resulting from injuries, developmental defects, paresis, paralysis and a number of diseases. The severity of foot deformity and disability can vary significantly - from almost complete preservation of function to severe disability. At the same time, even minor deformations of the foot have a negative impact on the overlying parts, cause pain, fatigue when walking, poor posture, premature fatigue of the muscles of the back and lower extremities and, ultimately, increase the likelihood of developing osteochondrosis and arthrosis of small and large joints lower extremities.
Treatment of foot deformities is carried out by orthopedists and traumatologists. Depending on the cause of the development of this pathology, neuropathologists, neurosurgeons, rheumatologists and other specialists may participate in the treatment.
The following main types of foot deformities are distinguished:
Horsefoot – accompanied by persistent plantar flexion. Active dorsiflexion at an angle of 90 degrees or less is impossible or difficult. In severe cases, the foot cannot be brought back to its normal position even by passive flexion.
Heel foot – characterized by persistent dorsiflexion. In severe deformities, the dorsum of the foot touches the front surface of the lower leg.
Hollow (rigid, supinated) foot - accompanied by an increase in the curvature of the longitudinal part of the arch. In severe cases, the patient rests only on the heads of the metatarsal bones and the calcaneal tubercle, while the midfoot does not come into contact with the surface.
Flat (soft, pronated) foot – characterized by flattening of the transverse or longitudinal part of the arch. With longitudinal flatfoot, the foot rests on the surface not with the outer edge, as is normal, but with the entire sole. Transverse flatfoot is accompanied by expansion of the anterior sections and an increase in the distance between the heads of the metatarsal bones.
In practice, a combination of several types of foot deformities is often observed. Along with the condition of the bones, joints, tendons and ligaments, the magnitude and type of deformation can be influenced by pathological changes in the overlying parts, especially the ankle joint.
A fairly common pathology. Clubfoot is accompanied by shortening of the foot and its supination, caused by subluxation of the ankle joint. May be congenital or acquired. Congenital clubfoot accounts for 1-2% of the total number of congenital developmental anomalies and is more common in men. Acquired clubfoot can develop as a result of paresis, paralysis, bone and soft tissue injuries. Both congenital and acquired clubfoot can be unilateral or bilateral.
Upon examination, 4 main types of foot deformation are revealed: plantar flexion, supination, pronounced longitudinal arch and metatarsal adduction. The most constant sign is the position of supination; the severity of other pathological changes can vary greatly. When walking, the main load falls on the outer side of the foot; with severe deformities, patients rely on the side and even the back surface.
Turning the foot inward and lifting the toe is impossible. Metatarsal adduction causes patients to turn their legs outward when walking to prevent the distal part of the foot from sagging. Calluses form in areas experiencing abnormal stress. The diagnosis is established taking into account data from an external examination, plantography, radiography of the foot and radiography of the ankle joint. If necessary, CT and MRI are prescribed. For paralytic clubfoot, consultation with a neurologist is necessary.
Treatment of congenital clubfoot begins from the first days of life. The leg is gradually brought into the correct position manually and fixed with a plaster cast. Initially, the dressing dressings are changed every 3 days, then the interval between plaster changes is increased. After moving the foot into the correct position and eliminating the subluxation of the ankle joint, the cast is replaced with night splints. If the desired effect cannot be achieved by the start of walking, special inserts are used. Upon reaching 3-4 years of age, exercise therapy is prescribed. If there is no result, surgical interventions are performed on soft tissues, and in severe cases, on bones.
Treatment tactics for acquired clubfoot are determined taking into account the cause and degree of foot deformity. If it is impossible to eliminate clubfoot using conservative methods, surgical interventions (arthrodesis of small joints) are performed. In some cases, the use of orthopedic shoes and special inserts is indicated. Patients are prescribed exercise therapy and physiotherapy, and are given referrals for sanatorium-resort treatment.
This pathology is a combination of several foot deformities and is characterized by flattening of the longitudinal arch, supination of the anterior parts and valgus position of the dorsum of the foot. May be congenital or acquired. Congenital clubfoot with flat feet is rare; acquired clubfoot is a consequence of insufficient elasticity of the ligaments and muscles of the foot. Predisposing factors are excessive professional stress, excess weight, paralysis, trauma and scar deformities.
Patients are concerned about pain that intensifies after prolonged exercise, and increased fatigue when walking. Upon examination, a “twisting” of the area between the dorsum and forefoot, flattening of the longitudinal arch and external clubfoot due to the valgus position of the foot are revealed. The talus bone runs along the inner surface of the joint (symptom of “double ankle”). To confirm the diagnosis, x-rays of the foot and plantography are prescribed.
At the initial stages, conservative therapy is carried out. If the patient can actively straighten the longitudinal arch, a special complex of exercise therapy is prescribed, it is recommended to wear comfortable, well-fitting shoes, and walk barefoot on grass, sand and stones. In cases where the longitudinal arch straightens only passively, it is necessary to use special liners and insoles. If there is severe deformation of the foot, wearing orthopedic shoes is recommended. If there is no improvement, surgical operations are performed on the bones of the foot and soft tissues.
It develops gradually and is caused by insufficient elasticity of the ligamentous apparatus and muscles that stabilize the forefoot. It manifests itself as an increase in the distance between the heads of the metatarsal bones. In this case, the head of the first metatarsal bone moves inward, and the heads of the II-V metatarsal bones move outward and towards the sole. This entails an increase in the load on the anterior sections and causes the formation of painful calluses. The toe flexors are constantly in a state of increased tension, which can lead to the formation of claw or hammer toes.
The diagnosis is clarified using plantography and radiography. Treatment is conservative. Patients with this foot deformity are recommended to perform special exercises and use inserts. Wearing orthopedic shoes is indicated only when combined with external clubfoot and when the position of the toes is abnormal.
The foot is in dorsiflexion, plantar flexion is impossible or limited. The pathology can be congenital, however, the calcaneal foot is not a true developmental anomaly of the lower extremities - its formation is due to the incorrect position of the fetus. In addition, this pathology can also be acquired, resulting from injury or paralysis. With a congenital deformity, there is a sharp deviation of the foot to the dorsal side, the foot is located at the anterior edge of the lower leg, active and passive abduction towards the sole is impossible. With an acquired pathology that develops as a result of paralysis, initially passive plantar flexion is retained in full. Subsequently, due to the predominance of extensor traction and overgrowth of the flexors, passive plantar flexion becomes impossible.
The diagnosis is made based on examination data, X-ray results, MRI and CT scan of the foot. Treatment of congenital pathology consists of gradual correction of the position of the foot using splints and redressing plaster casts. Acquired foot deformities are corrected surgically. In some cases, it is possible to use orthopedic shoes and night splints.
The foot is in plantar flexion, dorsiflexion is impossible or limited. The cause of the development of this foot deformity, as a rule, is flaccid paralysis of the triceps surae muscle. In addition, in some cases, the equine foot is formed with spastic paralysis due to the predominance of traction of the toe flexors. Sometimes pathological changes occur due to prolonged bed rest in a supine position or improper immobilization. Active dorsiflexion is not possible. In some cases, due to overstretching of some muscles and contracture of others, it is impossible to move the foot to a position of 90% in relation to the lower leg, even passively.
The diagnosis is made based on examination data; the condition of bones, joints and soft tissues is assessed using additional studies (radiography, electromyography, MRI, CT). Treatment for this foot deformity is usually conservative. For fresh paralysis, night splints and special orthopedic devices are used. If the foot cannot be passively moved into the correct position, retraining bandages are applied. While walking, bandages, orthopedic shoes, heel splints and special traction are used. If conservative measures are ineffective, surgical lengthening of the heel tendon or arthrodesis of the ankle joint is performed.
The foot is deformed due to the strengthening of the longitudinal arch. The pathology can be congenital or develop due to paralysis. Upon visual examination, a high rise is determined; the first sphenoid bone protrudes on the dorsal surface. Walking in regular shoes can cause pain due to compression of the tarsal area. With combined pathology (combination with finger deformation and transverse flatfoot), intense pain is possible even after a short walk or standing. To clarify the diagnosis, plantography, radiography and, if necessary, electromyography are performed. Foot cavities are usually treated conservatively, using inserts, insoles and orthopedic shoes. Surgical interventions are indicated only for severe foot deformities.
Please note that nothing is for sale on the zdorove.online website, but we can provide a link to the seller’s website.
Hallux valgus deformity often affects older people. However, it occurs among representatives of the younger generation. With hallux valgus, the big toe becomes bent, which interferes with normal life activities. The pathology hinders movement and causes severe discomfort.
The Valguflex fixative helps to cope with the disease. The drug relieves pain and swelling, eliminates other symptoms of pathology. You can buy Valguflex on the manufacturer's official website.
Valgus on the foot develops for the following reasons:
The bone can become deformed for other reasons.
The appearance of a lump on the thumb causes pain and redness in the affected area, which indicates the course of the inflammatory process. Symptoms of joint disease occur in the initial stages of development of the pathology and are pronounced. If you do not get rid of valgus immediately, the pathology provokes the appearance of arthritis and bursitis, which are difficult to treat.
You can suspect a joint deformity on the big toe based on the following signs:
Often at the initial stage of development of the disease, the clinical picture is blurred. The appearance of even one of the symptoms described above indicates the course of a destructive process in the joint of the big toe. It is recommended to begin treatment of hallux valgus as soon as signs of pathology appear. The success of finger recovery depends on this.
Valguflex, a remedy for hallux valgus, can eliminate the symptoms of the disease and restore the structure of the joint in one course of use. The product eliminates swelling and pain within 2 weeks, allowing a person to wear his favorite shoes again.
According to medical research, hallux valgus is more common in women. This is explained by the anatomical features of the skeleton. Moreover, the disease at one stage or another is diagnosed in approximately 70-80% of the planet's population.
In the traditional treatment of hallux valgus, massage and special baths are used. However, such measures can prevent the development of diseases of the musculoskeletal system. Massage and baths for a curvature of a joint temporarily improve a person’s condition, but do not restore the anatomically correct position of the finger.
For hallux valgus, specialized creams and gels are actively used. Such remedies are also effective only in combating the symptoms of pathology. Creams and gels relieve pain, relieve swelling and redness. But the joint remains deformed after using these drugs.
Another effective remedy is a bone retainer. A special device holds the joint in a certain position, thereby restoring its shape. Fixators successfully eliminate hallux valgus deformity in the initial stages of the disease.
Additionally, in the fight against pathology, tablet medications are used to strengthen tissues. Drugs in this group often damage internal organs.
In the absence of effect from conservative therapy, surgery is prescribed to restore the position of the joint. The procedure is considered effective for hallux valgus deformity. After surgery, the patient expects a long recovery period. Moreover, the pain and swelling of the tissues do not subside within several days.
Valguflex is a new and safe drug that can eliminate hallux valgus. The product does not cause an allergic reaction. Valguflex is based on ozokerite, which is used for various diseases of the musculoskeletal system.
The main feature of the drug is that it restores the anatomically correct position of the joint, simultaneously preventing the development of flat feet. The use of Valguflex must be combined with wearing a special retainer.
The patch is easy to use. It is attached to the finger using an elastic band and is additionally held in place with a clamp. The composition of the product includes only ozokerite, which warms the problem area, increasing blood flow to the damaged joint.
The patch has a complex effect. It suppresses the symptoms of hallux valgus and eliminates the factors that provoke the development of pathology. The components of the patch are made of hypoallergenic materials.
The action of Valguflex is based on the healing properties of ozokerite.
Wearing the patch together with an orthopedic fixator allows you to achieve the following results:
Real reviews of the bunion patch indicate that eliminating thumb deformity is quite simple. To do this, you need to install a clamp in the place where the lump sticks out. Next, you should attach the patch to your finger.
During treatment, it is recommended to wear comfortable and loose shoes. The patch and retainer can be removed at any time. Before using the product, you should consult your doctor.
The new patch can eliminate bunions that protrude from the big toe. It eliminates not only the symptoms of hallux valgus, but also the causes of its occurrence: trauma, salt deposits, etc. Regular wearing of the patch helps prevent the development of severe pathologies such as arthritis and bursitis.
Varus deformity of the lower extremities is an orthopedic pathology, manifested by an “O”-shaped curvature of the legs. Until 3 months of age it is considered normal. It is formed during the first year of life, when the child begins to walk.
Factors contributing to the development of deformity:
Varus deformity of the knee joints and feet is accompanied by a change in the shape of the bones of the lower extremities, curvature of their axis (legs varum samovar). When standing with your legs pressed together, your knees do not close, leaving space between them. The structure of the knee joint is disrupted: the external condyle increases and the internal condyle of the femur decreases. The meniscus is compressed and the joint space expands on the outside of the joint. When walking, the feet deviate outward, and the main load falls on their outer part. This inevitably leads to a disturbance in the child’s gait, which becomes awkward. As a rule, such children often fall and stumble, which leads to injuries.
This deformity is often confused by parents with clubfoot. With both pathologies, the child seems to have a clubbing when walking, however, these are completely different diseases. Clubfoot is a congenital pathology associated with intrauterine changes in the musculoskeletal system, varus position of the feet is an acquired disease.
In addition, there is also equinovarus foot deformity. People call it “horse foot”. With this pathology, the child does not stand on the entire foot, but only on its front part, as if walking on his toes.
Installation of normal and planovarus feet
To clarify the diagnosis, it is necessary to consult the child with an orthopedist. In addition to examining the child, in such cases, radiography of the lower extremities can be performed, which clearly shows the existing disorders.
The list of examinations includes plantography (allows you to determine the degree of inclination of the foot) and podometry (gives an idea of the load on the feet while walking).
Inspecting the shoes also helps to make a decision: varus deformity is characterized by greater wear on the outer side of the shoes, uneven wear of the heel (the inner side looks more intact, the outer side is more worn).
Depending on the severity of the pathology, degrees are distinguished:
In case of varus deformity, it is necessary to correct the condition in a timely manner. This is important for the formation of correct gait, the prevention of joint diseases and injuries in children. Changes in the structure of the foot and lower leg lead to disruption of the uniform distribution of the load. This affects the condition of the entire musculoskeletal system. Compensatory changes occur in the knee, hip joints, and spine.
Many parents, turning to an orthopedist, complain about club feet in children. Congenital clubfoot is the most severe form of the disease, which requires long-term treatment. Congenital clubfoot develops in the womb, the reason for this is developmental defects and hereditary predisposition.
Congenital clubfoot in children begins in the first weeks of a child's life, in contrast to varus deformity of the foot. In the latter case, therapy begins in adulthood, when the child begins to walk.
Many parents wonder how to correct clubfoot in a child. Clubfoot in children is treated on the recommendation of an orthopedist in the first weeks of life. The child's feet are bandaged to return the foot to a functional shape and to ensure its normal development in the future. If correction of the legs is started in a timely manner, the disease goes away completely and the baby’s legs become straight.
Treatment can be conservative and surgical. If a child has a clubbing when walking, action should be taken as early as possible.
Elements of conservative therapy:
If there is deformation, a massage is prescribed. You can take your child to a specialist for a massage of the legs and feet. Parents can master the massage technique and perform it themselves at home. This will make the procedure more accessible. It is necessary to massage the area of the lower back, buttocks, thighs, legs, and feet. It is better to perform massage before and after physical therapy. This will prepare the muscles and make the exercises easier.
Varus alignment of the feet can be easily corrected with the help of therapeutic exercises. Achieving a meaningful effect requires patience and persistence. The goal of such therapy is to change the pathological setting in the foot to a correct, normal one. To do this, it is necessary to monitor whether the child is performing the exercises correctly. You can start gymnastics with the simplest exercises. When the child masters the technique of performing them, new, more complex elements can be introduced.
In order for a child to enjoy performing physical therapy, it is better to conduct it in a playful way. Then the child will perceive gymnastics as a fun adventure, and not as a difficult and boring activity. The level of load and recommended exercises to perform should be discussed with your doctor or exercise therapy instructor.
Orthopedic correction helps the foot acquire the correct alignment. Varus foot deformity in children requires wearing special shoes, which differ in their features:
This helps keep the foot in its normal position, preventing it from moving outward. Wearing such shoes will correct the existing deformation. You can purchase such shoes only after consulting a specialist. Incorrectly selected shoes can aggravate existing deviations.
If conservative methods are ineffective, surgical correction is resorted to. This type of treatment is used for severe deformities. The operation is usually performed at the age of 5-7 years. The deformity is corrected by performing an osteotomy and applying an Ilizarov apparatus. The duration of surgical treatment along with the rehabilitation period can last up to a year.
Prevention of varus deformity is carried out based on the causes of this disease: