PART I - STRUCTURAL ENGINEERING: SHEAR CENTRE DETERMINATION

APPARATUS-

The shear centre specimens are constructed from 16SWG (1.63 mm thickness) sheet steel with welded-on end plates perpendicular to the beam longitudinal axis. At the mid-span of each beam a transverse loading plate is rigidly fixed so that a load hanger can be hung in a series of holes which are at different transverse eccentricities relative to the beam section. Two end support brackets enable the test specimen to be set up as a fixed beam. A bracket carries two dial gauges, with toilers instead of anvils, to register the displacement of the top edge of the transverse loading plate. The experimental arrangement eliminates warping of the specimens as they bend and rotate about a longitudinal axis.

OBJECT-
The object of the experiment is to find the shear centre of a selection of beam cross-sections. The four provided are a channel, a semi-circle, an equal angle and a zed.

PROCEDURE-

By using two dial gauges to measure the vertical displacement of each top corner of the central loading plate it is possible to derive the rotation of the plate in its own plane as the load is applied at different eccentricities to the centroid of each section. The 'no load' readings should be taken without the load hanger in place.

For each of the four sections in turn record the front and rear dial gauge readings as a fixed load plus the hanger is applied at the eleven positions across the loading plane. Use 40N for the equal angle and 100N for the other sections. Note the relation of the load position to the vertical part of each section.

RESULTS-

The twisting of the beam can be evaluated in terms of the tilt of the transverse plate over the 200mm separating the two dial gauges. Thus the rotation is proportional to y_l - y_r, where the displacement y is the difference between the loaded and unloaded dial gauge readings. Take care with the -ve and +ve signs which will reverse as the load is moved from front to rear of the loading plate.

For each section, construct a graph of rotation against load position, Draw a best-fit straight line through the rotation plots and use it to find where the load should be applied for zero rotation. Hence establish the eccentricity of the shear centre in relation to the vertical part of each section.

State the shear centre eccentricities for the angle and zed sections and calculate the eccentricity for the channel (e = 3b²/h(1+6b/h)) and semi-circle (e = r(4/π-1)).

CONCLUSIONS-

Compare the theoretical and experimental values of shear centre eccentricity.

PART II - STRUCTURAL ANALYSIS: UNSYMMETRIC BENDING

APPARATUS

The mild steel cantilever has a nominal section 20x10mm and is 600mm long. It is welded to a rotating clamp which fits in a block attached to the vertical side of the Fame. The block is positioned so that the axis of the rotating clamp is about 130mm above the base of the frame. The angular markings on the clamp base are figured sot that the 90^o and 180^o locations correspond to bending about the x-x and y-y axes respectively.

At the other end of the cantilever is a peg set into the centre of the section. A self-aligning ball bearing is held on the peg by a screw, and provides a means of applying a vertical load. The bearing housing has an outer part spherical surface so that the dial gauge reading of its deflection are not altered by the slope at the end c the cantilever.

Two dial gauges are mounted at right angles to each other on a circular plate which rotates on a central shaft. An extension of the shaft, in the form of a point, provides a reference for the initial positioning of the plate. The bracket supporting the plate permits vertical and horizontal adjustments to be made in order to align the reference point to the centre of the peg on the free end of the cantilever. Note that the angular markings on tile plate are figured so that the dial gauges X and Y, fixed at the 0^o and 90° locations will measure either d_v or d_i at settings of 90^o and 180^o. When the same angular reading is set for the cantilever clamp and the dial gauge plate, the gauge X and Y will read d_x and d_y respectively with reference to the cantilever principal axes x-x and y-y in whatever direction these axes lie.

OBJECT-

To compare the theoretical and experimental deflections as the loading direction is changed, P

ROCEDURE-

Start with the fixed end and dial gauge plate both at the same reading of 45^o and centralise the plate. Take the dial gauge reading before and after a loading of 20N on the hanger. Repeat this for each 15^o increment between 45^o and 225^o, keeping the fixed end plate always at matching angular reading and the plate re-centred each time.

RESULTS-

The deflections obtained should be plotted as ordinates on a graph where the x-axis is the angular setting. Draw the best fit curves through the points. Compare the experimental resultant deflections with theory by calculating and plotting deflections obtained from components determined (taking E = 210 kN/mm²) as:

d_x = (WsinθL³/3EI_x) and d_y = (WcosθL³/3EI_y)

DISCUSSION AND CONCLUSIONS-

Compare the observed and expected deflection behaviour in terms of the directions and relative sizes of d_x, d_y.

Attachment:- Assignment.rar