Stress Analysis Report

The goal of the beam project is to design and construct a beam that can hold a given amount of weight without breaking. The beam is required to hold a concentrated load of 375 lbf on the X-axis and 150 lbf on the Y-axis. The maximum allowable weight of the beam is 250 grams. The maximum allowable deflection for the beam is 0.230 in. and 0.200 in. for the X and Y-axis respectively. The beam is required to be 24 in. in length, and it will be tested on a simply supported configuration spanning 21 in. All calculations are to be done under the assumption that the density of basswood is 28 lbm/ft3 and the modulus of elasticity for basswood is 1.46x106 lbm/in2. Given the constraints of a spending cost of $10.50, a maximum beam weight of 250 grams,

After the analysis on the first design brought to light the zero for members, it was decided that these members should be removed. In order to combat the flex of such a simple design the decision was made to double the thickness. This design would have the same outer frame of two triangles with a height of 20 centimeters and a width of 40 centimeters. Instead of being spaced five centimeters apart the wood be bonded directly together using Gorilla Glue. Balsa wood, a very lightweight wood with properties similar to a dense foam, was used for the main supporting member. Basswood, a lightweight yet firm wood, was used for the horizontal member. The final design added a triple layer sheet of balsa wood to rear side of the truss. This balsa sheet was added for the purpose of mounting and supporting the main structure. Additionally, a five centimeter square frame of bass wood was added at the end of the boomilever to place the loading block for testing. Once this design was implemented two key issues were discovered. First, due to the properties of the bass wood and balsa wood it was obvious that the placement needed to be reversed. The bass wood should be used for the hypotenuse and the balsa wood should be used for the

in the xy-plane is equal to the radius (R) of the beam pipe, as shown in Fig.~\ref{beampipeconversion},

The specimen ends were not thick or had moving wedge grips to keep it secure in the holders of the servo-hydraulic load frame. The movement of the specimen in the machine causes some of the data to be an inaccuracy. Also, the transverse strain causes issues with the strain gages that are called transverse sensitivity. The transverse sensitivity affects the accuracy of the data that is being collected for the transverse strain more than the longitudinal strain. This is greatly seen in the percent difference in the strain values such as in one case the Longitudinal strain was .4% while the transverse strain was 30%. Another issue with the strain gages was that if the strain gages weren’t properly placed on the specimen the data accuracy would

The programmed algorithm is shown in Figure 6.The program was developed using LabVIEW System design software. The entire experimental set-up is shown in Figure 7.

Fig. 1. (a) Schematic view of the structure at rest. (b) Schematic view under external acceleration

A beam of mass mb = 10.0 kg, is suspended from the ceiling by a single rope. It has a mass of m2 = 40.0 kg attached at one end and an unknown mass m1 attached at the other. The beam has a length of L = 3 m, it is in static equilibrium, and it is horizontal, as shown in the figure above. The tension in the rope is T = 637 N.

{N} and {M} are the generalised stresses can can be expressed as membrane strains and curvatures by using the laminar stress-strain relationship and Love Kirchhoff hypothesis.

This report aims to describe the experiment performed to investigate the stiffness of a channel section, and in particular calculate the flexural rigidity (EI) of the beam by two different sets of calculations based on the results gained in the experiment. The EI of an object is used

where r_1 is the radius from left side of the beam and r_2 is the radius from the right side.

Below are two tables in which I have recorded the data which I obtained during the experiment. The first table reflects the Relationship between the deflection/flexion of the cantilever and the mass of the load and the second table reflects the relationship between the flexion of the cantilever and the length of the cantilever.

Where P is the applied force, L is the length of beam, E is the modulus of elasticity of aluminum, and I is the moment of Inertia.

A Chakraborty et al [1] have studied the thermo-elastic behavior of functionally graded beam structures based on the first-order shear deformation theory and these properties are varying along its thickness. The governing differential equations are used to construct interpolating polynomials for the element formulation. To determine various stresses, both exponential and power-law variations of material property distribution are used. Thermal behaviors of functionally graded beam (FGB) by taking the distribution of material properties in exponential function were analyzed by GH Rahimi and AR Davoodinik [2]. The steady state of heat conduction with exponentially and hyperbolic variations through the thickness were consider for the use of thermal loading. They found that thermal behavior of both isotropic beam and functionally graded beam depend up on the temperature distribution.

The plate under study is a rectangular plate simply supported at four ends with load force at it extremes, the study aims to find the nodal displacement of the plate caused by the load. Also the plate was modeled in FEA software for comparison reason and to check the algorithm accuracy, the plate specification is as follows:

“Technology takes a new leap every day. New designs and components will require high resolutions for monitoring health and structural characteristics and also to test their performance. The quality of new devices directly implies on the level which we can measure their performance. Conventional techniques which have been lasting for so long will not provide the high resolutions needed for new and advancing designs for the measurements of different quantities, mainly strain. Some of the conventional methods like Classic foil strain gauges and accelerometers have been trusted and used for several years to measure the strains on various buildings, air planes, human body, and many others, which end up failing during harsh conditions.