How Does the Arch Machine Work - Lab Report Example

Structural Analysis Name: Institution: Abstract The arch instrument is more advantageous and effective as an instrument than the beam because it carries much load. Compared to the beams, arches were constructed with small, easily portable bricks or stones which made them easier to use unlike beams which were made of larger monolithic stone beams or lentil. Their advantages are why they were preferred by Romans as they built bridges, aqueducts and other architectural activities and to date they are still the most preferred and opted for instruments in architectural activities. How does the arch machine work? It is basically a machine used to carry load. A loaded arch is acted upon by forces of gravity putting a pressure on the arch that acts downwards on the arch, causing a compression effect rather than pulling the arch apart. The arch is acted upon by both horizontal and vertical reaction forces but if the horizontal forces also called thrust are not properly contained by constraining, it may lead to the arch collapsing (Boresi, Schmidt, & Sidebottom, 1993). There are three main types of arches that are used in architectural activities. They are the three hinged, the two hinged and the hingless arches. As suggested by their names, the arches are classified based on the number of hinges they bear. The three hinged arch was used in the earlier 19th century especially on long life structures because of the confidence with which the analysis of such analysis could be carried out but with time and more technological advancement and development in structural analysis, the architects adopted the use of two hinged and hingless arches. Use of the two hinged arch in analysis is a statistically indeterminable structure. The horizontal reaction therefore in this two hinged arch is treated as redundant and evaluated in a way of the least work. In the subsequent experiments, we majorly dwell on the analysis of the two hinged arches and also explained is how to calculate internal forces (Milton, 2002). Experiment No. 1 Aim: This experiment’s main aim is to ascertain the strain in an externally loaded beam using a strain gauge indicator and to further support this theoretically. Apparatus: weights, measuring scale, verniar calipers, a stain gauge indicator and a hanger. Introduction A beam loaded with some external loadings produces moment and shear force at each each strain. While this is happening, the bending will always behave as if to resist this bending action through internal forces which are referred to as the bending stresses (Tan, 1994). The simple assumptions theory will always assume the following: that materials used in the beam are isotopic and perfectly homogeneous hence the elastic properties are similar in all the directions of the beam, the beam will always stretch to its elastic limit thus is obeys the Hook’s law, that the transverse plane remains even after the ending action and that the in both the tension and compression, the value of young’s modulus of elasticity is the same. The use of the digital strain indicator is to determine the amount of strain in static condition. Used alongside the basic internal arms and the bridge network, the digital strain indicator gives an exact value of the strain. Different types of strain gauge can be used, and when the resistance strain gauge is used, then a wire used when stretched elastically will always change, altering its length and diameter dimensions, a factor that is applied in measuring resistance change when different load amounts are applied. The strain is then calculated using the Hook’s laws and formulae. Distrain is also a factor that will come to play and is always measured. The Distrain indicator is used to measure the levels of the extreme fiber at any one particular section. This is done to determine the levels of strain by using amplifier and digital display among others (Petroski, 1996). The number of strain gauges are determined by the number of arms in that a two arm bridge will use a two strain bridge and will show values twice the actual values while if the four armed bridge was used, then a four strain gauge will be used and will produce a value quadruple the actual value. Procedure The beam was mounted with a hanger at the position we choose with the strain gauges over it placed to properly support and connect the strain gauges to the digital indicator in accordance with the circuit diagram. The digital indicator is connected to 230 colts 50Hz single phase AC power supply and then the switch on the apparatus in turned on. Then, using the two four arm bridge, we balanced the bridge until the reading is 000. We then pushed the GF READ switch and adjusted the gauge factor to tally with that of the strain gauge used 2.00 after which we just applied the different loads on the hanger in an ascending manner as we noted the corresponding strain value. Results The theoretical value and the observed values of strain are similar as from the observational table. Experiment No. 2 Aim: We wanted to study the behavior of different types of columns and find the Euler’s buckling load in each. Apparatus: Dial gauge, bucking apparatus, weights, scale and vernier calipers Introduction When the load is added unto a column, the member may fail by crushing or buckling depending on materials used in its cross section and length. Members that are usually longer compared to the lateral dimensions will always fail by bucking, so any member with signs of buckling will often fail with a slightest increase in its load. The amount of load at which a member will buckle is termed as crushing load (Slaughter, 2001). These circumstances are always bound to have four outcomes depending on the support conditions. In each of the four anticipated outcomes, the effective length for each will be given as: 1. le = L/ 2 if the two ends are really fixed 2. le = L/√ 2 if one of them is fixed and the other is pinned 3. le = L if both ends are pinned 4. le = 2L if only one is fixed and other is free Procedure We pinned on the wooden board behind the column a graph paper after which we applied a load on top of columns in a gradual increasing manner until the point when we begin to observe abnormal deflections and give us the buckling load. We then noted the buckling load for all of the four columns. We also traced the shapes of the deflected columns on a piece of paper and marked the points of change of curvature on those curves and measured the effective length for each. We then calculated the theoretical real effective lengths and compared them with the observed values. Results From the experiment, we concluded that the Euler’s and theoretical buckling load for each case is equal. Experiment No. 3 Aim: To observe the two hinged arch’s horizontal displacement of the roller end in a system of loading and compare this to the analytic values. Apparatus: Weights, hanger, dial gauge, two hinged arch apparatus, scale and a venier caliper. Introduction Being a statistically indeterminate structure of the first degree, a two hinged arch’s horizontal thrust is a redundant reaction which is obtained using strain energy methods. The two hinged arch tool is usually made determinate through treating it as a supported curved beam and its horizontal thrust treated as a redundant reaction (Simo & Hughes, 1998). Under the influence of the external load, the arch will spread out while the redundant reaction, the horizontal thrust, will be obtained using the strain energy method. Procedure We placed a 0.5kg load on the central hanger of the arch to prevent any slackness and then set our reading on the dial gauge to zero. Next, we placed a 1kg weight to the hanger and recorded on a table the horizontal movement of the roller end as we increased the load by 1kg after very individual recording. Readings were also recorded on the table as the unloading was being done. We then plotted a graph of load versus displacement and compared it with the theoretically given values which are obtained by use of the horizontal displacement formulae. We then moved the lever into contact with 200g hanger in a 4/1 ratio position having placed a 1kg load on the first hanger and set the initial reading of the dial gauge to zero. We then placed an additional 5kg load on the initial hanger gently and observed the dial gauge reading after which we returned the gauge reading to zero by placing additional loads to the lever hanger, a load totaling to w kg. Therefore, the experimental figures will therefore be 4w/5. The process is then repeated for all. We then plotted the influence line ordinates after which we compared the figures with the theoretical values. Results: We observed that the observed and horizontal displacement were almost similar. NOTE: We should apply the loads in the course of the experiment without jerk and that the experiment should be carried out away from vibration and other disturbances. Conclusion The two hinged arch is a statistically indeterminate structure. To a certain degree, the horizontal reaction treated redundant is assessed by the means of the least work while the strained energy stored in the two hinged arch when the disfiguration is taking place is provided (Symon, 1971). References Boresi, A. P, Schmidt, R. J., & Sidebottom, O. M. (1993). Advanced Mechanics of Materials. New York: Wiley. Milton, G. W. (2002). The Theory of Composites. Cambridge: Cambridge University Press. Petroski, H. (1996). Invention by Design: How Engineers Get from Thought to Thing. Cambridge, MA: Harvard University Press. Slaughter, W. S. (2001). The Linearized Theory of Elasticity. London: Birkhäuser. Simo, J. C., & Hughes, T. J. R. (1998). Computational Inelasticity. London: Springer. Symon, K. (1971). Mechanics. Reading, MA: Addison-Wesley. Tan, S. C. (1994). Stress Concentrations in Laminated Composites. Lancaster, PA: Technomic Publishing Company. Read More

1 Aim: This experiment’s main aim is to ascertain the strain in an externally loaded beam using a strain gauge indicator and to further support this theoretically. Apparatus: weights, measuring scale, verniar calipers, a stain gauge indicator and a hanger. Introduction A beam loaded with some external loadings produces moment and shear force at each each strain. While this is happening, the bending will always behave as if to resist this bending action through internal forces which are referred to as the bending stresses (Tan, 1994).

The simple assumptions theory will always assume the following: that materials used in the beam are isotopic and perfectly homogeneous hence the elastic properties are similar in all the directions of the beam, the beam will always stretch to its elastic limit thus is obeys the Hook’s law, that the transverse plane remains even after the ending action and that the in both the tension and compression, the value of young’s modulus of elasticity is the same. The use of the digital strain indicator is to determine the amount of strain in static condition.

Used alongside the basic internal arms and the bridge network, the digital strain indicator gives an exact value of the strain. Different types of strain gauge can be used, and when the resistance strain gauge is used, then a wire used when stretched elastically will always change, altering its length and diameter dimensions, a factor that is applied in measuring resistance change when different load amounts are applied. The strain is then calculated using the Hook’s laws and formulae. Distrain is also a factor that will come to play and is always measured.

The Distrain indicator is used to measure the levels of the extreme fiber at any one particular section. This is done to determine the levels of strain by using amplifier and digital display among others (Petroski, 1996). The number of strain gauges are determined by the number of arms in that a two arm bridge will use a two strain bridge and will show values twice the actual values while if the four armed bridge was used, then a four strain gauge will be used and will produce a value quadruple the actual value.

Procedure The beam was mounted with a hanger at the position we choose with the strain gauges over it placed to properly support and connect the strain gauges to the digital indicator in accordance with the circuit diagram. The digital indicator is connected to 230 colts 50Hz single phase AC power supply and then the switch on the apparatus in turned on. Then, using the two four arm bridge, we balanced the bridge until the reading is 000. We then pushed the GF READ switch and adjusted the gauge factor to tally with that of the strain gauge used 2.

00 after which we just applied the different loads on the hanger in an ascending manner as we noted the corresponding strain value. Results The theoretical value and the observed values of strain are similar as from the observational table. Experiment No. 2 Aim: We wanted to study the behavior of different types of columns and find the Euler’s buckling load in each. Apparatus: Dial gauge, bucking apparatus, weights, scale and vernier calipers Introduction When the load is added unto a column, the member may fail by crushing or buckling depending on materials used in its cross section and length.

Members that are usually longer compared to the lateral dimensions will always fail by bucking, so any member with signs of buckling will often fail with a slightest increase in its load. The amount of load at which a member will buckle is termed as crushing load (Slaughter, 2001). These circumstances are always bound to have four outcomes depending on the support conditions. In each of the four anticipated outcomes, the effective length for each will be given as: 1. le = L/ 2 if the two ends are really fixed 2.

le = L/√ 2 if one of them is fixed and the other is pinned 3. le = L if both ends are pinned 4. le = 2L if only one is fixed and other is free Procedure We pinned on the wooden board behind the column a graph paper after which we applied a load on top of columns in a gradual increasing manner until the point when we begin to observe abnormal deflections and give us the buckling load.

Read More