CN201829094U - Bar-bar structure reciprocal-displacement theorem experimental device - Google Patents

Abstract

The utility model discloses an experimental device for the mutual displacement theorem of rod structures, which is assembled from a left arch piece, a right arch piece, a hinge, a rigid arm with a screw hole and a screw rod, a drag cable, and a cylindrical roller. The arch is equipped with several weight hooks and the tiny test surface of the displacement gauge; the hinge is composed of a cylindrical pin barrel at the top of the left arch and a slender cylindrical pin shaft at the top of the right arch, and there is a downward protruding belt screw at the bottom of the hinge. Rigid arm for hole and screw. Loosening or tightening the screw on the rigid arm can transform the assembled structure between a statically determinate three-hinged arch and a statically determinate two-hinged arch. By measuring the displacement of the three-hinged arch or two-hinged arch when the external weight acts on a certain position, and then reversing the position of the weight and the displacement meter, the displacement can be obtained again, and the two displacements are always equal. reciprocity theorem. The utility model has the advantages of simple structure, convenient operation, high testing precision, and can intuitively and clearly reflect the inherent characteristics of structural displacement mutual equality.

Description

Bar bar displacement structure reciprocal theorem experimental provision

Technical field

The utility model relates to the experimental provision that a kind of displacement measures and verifies, relates in particular to a kind of experimental provision that measures the member structure displacement and verify the displacement reciprocal theorem.

Background technology

Member structure comprises beam, rigid frame, truss, arch and unitized construction, is the version that is most widely used in the engineering practice.The displacement reciprocal theorem is the ultimate principle in the member structure mechanics, and it has reflected the internal relation between linear deformation structure stress and the distortion, is one of important mechanical characteristic of member structure (in fact also being applicable to other solid structures).

The displacement reciprocal theorem relates to the two states of same linear deformation structure, and two states has acted on an external force (can be generalized force) respectively.Because the structure of two states all is in balance, so according to the principle of virtual work, the external force of first state just equals the virtual work done in the distortion (flexural deformation, axial deformation and detrusion) of internal force (moment of flexure, axle power and shearing) at second state of first state in the virtual work of being done in the displacement of second state; As a same reason, the virtual work done in the displacement of first state of the external force of second state equals the virtual work that the internal force of second state is done in the distortion of first state.According to the The deformation calculation formula under the external force effect, the virtual work that the internal force under the two states is done in the distortion of another state equates that like this, the virtual work that the external force of two states is done has also just equated in the displacement of another state.If the external force of two states is unit force, just can push away: the corresponding displacement of the unit force with first state that the displacement that the unit force with second state that the unit force of first state causes is corresponding (or being interpreted as the Influence of Displacement coefficient) causes with regard to the unit force that equals second state, Here it is displacement reciprocal theorem.

This shows that the displacement reciprocal theorem is derived indirectly by the principle of virtual work, its essence is that the mutual external force virtual work of doing of two states equates.In present teaching practice, the displacement reciprocal theorem all adopts the mode of theoretical analysis and derivation to lecture.Though this mode is essential, also come with some shortcomings, for example simple and clear inadequately, lack physical verification, it is deep etc. that the beginner often understands.If can create a kind of simple and easy to do experimental provision, the displacement of two states is measured, and in view of the above phenomenons such as displacement is mutual are carried out physical verification, will obtain more directly perceived, vivid teaching efficiency.

Summary of the invention

For the intrinsic characteristic of showing that intuitively, visually bar bar displacement structure is mutual etc., the utility model provides a kind of bar bar displacement structure reciprocal theorem experimental provision.This device is adding counterweight (or other weights) displacement of displacement meter position when acting on a certain position by the static determinacy three-hinged arch (can change hyperstatic two-hinged arch into) of measuring a band pull bar, again the position of counterweight and displacement meter is exchanged, redeterminate displacement, thereby obtain the displacement reciprocal theorem that two displacements equate all the time.

The purpose of this utility model is achieved through the following technical solutions: the utility model comprises firm arm, drag-line, the cylindrical roller of left side arch sheet, right arch sheet, hinge, band screw and screw rod.The arch sheet is installed a hook respectively along the lower surface at 1/4,1/2,3/4 and position, top of horizontal projection length on a left side, and the upper surface center of relevant position processes the rectangle minute water plane of a 3mm * 3mm respectively.Can hang scale pan and counterweight (or other weights) on the hook, displacement meter (dial gauge) can be installed on the minute water plane.Hinge is assembled by the cylinder plugs tube and the cylinder plugs axle on left and right arch sheet top, and latch tube bottom surface and bottom surface, bolt axle end are stretched out firm arm downwards, and just the arm top has screw and screw rod respectively.Cylindrical roller is installed on the thin rod bearing of right arch sheet lower end Y shape opening.About arch plate shape symmetry, linear is second-degree parabola; Arch sheet and drag-line are all made of steel.

Insert left side arch sheet latch tube by the right side being encircleed the sheet bolt axle, again two arch sheet bottoms are connected with drag-line, just formed a band drag-line three-hinged arch structure that geometry is constant; The roller of right-hand member is exactly a slip hinged-support, has guaranteed that the three-hinged arch right-hand member can be free to slide in the horizontal direction.If with about the firm arm that stretches out downwards of arch hinge place, sheet top tighten with screw rod fixing, about arch sheet top can not relatively rotate, the structure of Zu Chenging just is transformed into a two-hinged arch structure (being three-hinged arch originally) of being with drag-line like this.

The beneficial effects of the utility model are:

1) experimental provision is a fabricated construction, can dismantle immediately and assembly unit, and simple structure is easy to carry and in the operation of different occasions, demonstration.

2) select for use arch structure as experimental provision, existing drag-line straight-bar (chain bar), again curved bar (beam type bar) arranged, the distortion that causes displacement promptly comprises flexural deformation, comprises axial deformation and detrusion again, we can say comprehensive stressed and deformation behaviour that reflects the dissimilar members of member structure.

3) arch structure can be changed between the three-hinged arch of static determinacy and hyperstatic two-hinged arch, therefore can check the displacement of statically determinate structure mutual etc., can check the displacement of hyperstatic structure mutual etc. again.

Description of drawings

Fig. 1 is the utility model experimental provision structural representation;

Fig. 2 (a), Fig. 2 (b) are respectively the front elevation and the vertical views of the firm arm of the hinge on left and right arch sheet top and band screw that stretches out downwards and screw rod;

Fig. 3 is a right arch sheet bottom roller structural side view;

Among the figure, 1. sheet is encircleed on a left side, 2. right arch sheet, 3. hinge, 4. firm arm, 5. hook, 6. minute water plane, 7. displacement meter fixed support, 8. displacement meter (dial gauge), 9. scale pan and counterweight, 10. drag-line, 11. stay cable end micro screws, 12. nut, 13. rollers, 14. experimental provision platforms, 15. hinge latch tubes, 16. stretch firm arm under the latch tube, 17. screws, 18. hinge bolt axles are stretched firm arm under the 19. bolt axle ends, 20. screw and screw rod, 21. right arch sheet Y shape openings, 22. roller bearings.

Embodiment

The utility model is described in further detail below in conjunction with drawings and Examples, and it is more obvious that the purpose of this utility model and effect will become.

As depicted in figs. 1 and 2, the bolt axle 18 that the right side is encircleed sheet 2 inserts within the latch tube 15 of left side arch sheet 1, the micro screw 11 that will be fixed on drag-line 10 other ends on the right arch sheet again passes the aperture of arch sheet bottom, a left side, the nut 12 of regulating the arch sheet outside, a left side makes the length of drag-line 10 at the arch springing place reach design length l, drag-line to the vertical range of vault reaches design sagitta f, form band pull bar (drag-line) three-hinged arch that geometry is constant thus, the shape of arch meets following second-degree parabola shape:

$y=\frac{4f}{l^2}x(l-x)$

In the formula x axle along drag-line to the right, the y axle straight up, initial point is located at the drag-line left end.

1) measurement of three-hinged arch Influence of Displacement coefficient and displacement wait checking mutually

Select arch sheet top to have the position on minute water plane, at this position displacement meter 8 is installed with displacement meter support 7, the pointer that makes displacement meter vertically and aim at the center on minute water plane reads the initial reading of displacement meter; Optional another place has the position of hook scale pan and counterweight 9 is added on the hook 5, read the reading of displacement meter, measure the displacement of displacement meter position when this position applies vertical force, this displacement is exactly the Influence of Displacement coefficient of this situation divided by the weight that applies, and is designated as δ _Ij

The position of counterweight and displacement meter is exchanged.At first removal scale pan and counterweight move to the former position (upper surface of relevant position) that applies scale pan and counterweight with displacement meter, read the initial reading of displacement meter; Again scale pan and counterweight are applied to the position (on the bottom hook of relevant position) that former displacement meter is installed, remeasure out displacement.This displacement is exactly the Influence of Displacement coefficient that the back situation is exchanged in the position divided by the weight that applies, and is designated as δ _JiThe displacement of two kinds of situations of cause is same static determinacy three-hinged arch and is in the displacement of equilibrium state, so δ is arranged _Ij=δ _Ji, just reproduce and verified the displacement reciprocal theorem of statically determinate structure thus.

2) measurement of two-hinged arch Influence of Displacement coefficient and displacement wait checking mutually

On above-mentioned basis of having assembled the three-hinged arch structure of finishing, the screw rod of stretching under the sheet top on the firm arm 19 (20) is encircleed on the right side to be screwed under the left side arch sheet and to stretch in the screw 17 of firm arm 16, locking two firm arms, even its top can not relatively rotate, so just obtained the two-hinged arch experimental provision of a hyperstatic band drag-line.Repeat above-mentioned same measurement, just can verify the displacement reciprocal theorem of indeterminate two-hinged arch structure at three-hinged arch.The influence that the measurement result of this experimental provision is not subjected to other external factor substantially utilizes dial gauge as displacement meter, and its test error can be controlled in below the 0.01mm.Therefore this device is not only easy to operate, and has reliable and stable, the accurate high characteristics of test.

Claims (3)

1. A rod structure displacement reciprocal theorem experimental device is characterized in that it is assembled by left arch sheet, right arch sheet, hinge, rigid arm with screw hole and screw rod, dragline, cylindrical roller; A hook is installed on the lower surface of the characteristic section of the left or right arch for hanging the weight plate and weights; there is a rectangular tiny horizontal surface at the center of the upper surface at the corresponding position for installing the displacement gauge. 2. The rod structure displacement reciprocal theorem experimental device according to claim 1, characterized in that, the hinge is made up of a cylindrical pin cylinder at the top of the left arch and a cylindrical pin shaft at the top of the right arch; A rigid arm protrudes downwards from the bottom, and a screw hole is provided at the top of the rigid arm; a rigid arm extends downwards from the end of the pin shaft, and a screw hole and a screw rod are provided on the top of the rigid arm. 3. The experimental device for the displacement equivalence theorem of rod structures according to claim 1, characterized in that there is a Y-shaped opening at the lower end of the right arch, and a thin rod bearing is connected to the opening, and a cylindrical roller is installed on the bearing. the

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