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Design of a Beam

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Stress Analysis PBL Design of a Beam Group 17 Abstract The report centred around the design of a beam to hold a load in a real-world scenario. First the topic is introduced, then the background theory and statistics of the materials are presented. The bulk of the calculations were performed by computer as presented in the discussion section but these were also performed by more theoretical methods to check the results were consistent. Various cross-sections are considered along with two different ways of mounting the beam along with the environmental and financial advantages of the particular materials. The report then concludes based on the findings presented in the discussion that the load should be distributed on a mild steel beam with an "I" shaped cross-section. Contents 1. Abstract Page 2 2. Introduction Page 3 3. Background Theory Page 4 4. Calculations Stress Page 9 Cross Section Page 21 5. Discussion Stress Page 25 Cross Section Page 28 Safety Factors Page 20 Environment Page 30 6. Conclusions Page 31 7. Final Design Page 32 8. References Page 33 Introduction When designing a supportive structure of any kind upon which a load will be applied, there are many things to consider, which fall into two main categories - the specification of the structure and the types of forces that the structure will experience. The structure itself must be able to fulfil the criteria given in order to support the applied load. The list of criteria usually includes: * Shape - dimensions, shape of cross-sectional area * Material - hardness, stiffness, durability, chemical composition, life span, ability to resist environmental damage (e.g. corrosion). * Cost - Is the design feasible? Will using cheap material affect the support capability of the structure? Does the complexity of the design affect the cost? * Safety - what Health and Safety factors need to be taken into consideration? If the structure is external, will weather-related safety factors need to be considered?


Shear force and Bending moment diagram is as follows for concentrated: V (figure 13) M (figure 14) Shear force and Bending Moment is calculated for Distributed load In this case load intensity it taken as 12.5kNm. Load is uniformly distributed in 2m of the beam. It is assumed for calculation of reaction force that load of 25kN will be acting at 2m from. 25kN 4m 1m (figure 15) Resolving forces in horizontal direction There are no forces other than horizontal provided by the pin joint. Therefore= 0 Resolving forces in vertically direction To find the vertical reactions and moment about point A is calculated. 4= 50kNm =12.5kN Therefore = 12.5kN Shear force is calculated as follows * Cut is imagined at 1m from (figure 16) * Cut is imagined at 2m from 1.5m 0.5m (figure 17) * Cut imagined at 3m from 12.5kN/m 1m 2m (figure 18) 25kN 2m 1m (figure 19) * Cut imagined at 4m from 12.5kN/m 1m 2m 1m (figure 20) 25kN 2m 2m (figure 21) * Cut imagined at 5m from V (figure 22) M (figure 23) Bending stress is calculated using formula given below. = Bending stress M = Maximum moment = Moment of inertia y = thickness/2 Bending stress is calculated for the concentrated load M = 25kNm = = = b = breath of the beam b = 5m = 5000mm d = depth of the beam = 0.4m = 400mm = = y = y = 200mm for Distributed load. Bending stress is calculated for the concentrated load M = 18.75kNm = = = b = breath of the beam b = 5m = 5000mm d = depth of the beam = 0.4m = 400mm = = y = y = 200mm Cross Section Euler's Buckling Theorem allows us to determine theoretically the load that can be applied to a beam before it deforms by bending.


High temperature: can cause the material began to expand its structure byand. If the expansion is too large, then fatigue will occur and crack produced. Corrosion environment is the atmosphere. Moisture containing dissolved oxygen is the primary corrosive agent. [5] Metallic corrosion is classified into eight forms uniform, galvanic, crevice, pitting, intergranular, selective leaching, erosion-corrosion and stress corrosion. Aluminium is less corrosive than the steel because of its oxide layer that acts as physical barriers to corrosion. Conclusions * A mild steel beam deflects less than an aluminium beam when carrying the same load. * Both mild steel and aluminium have a safety factor co-efficient that is greater than 1, demonstrating their suitability for this scenario. * Aluminium has an environmental advantage over mild steel as an oxide layer acts as a barrier to corrosion. * Mild steel costs much less than aluminium per kg (figure 4). Although both materials have their own advantages, based on the discussions in this report and the group's opinion that price is the most important factor, mild steel was selected as the material of choice for the beam in the final design. * For both materials, a beam subjected to a distributed load deflects less than one subjected to a point load (if the screen in the scenario were supported by some type of pillar). Of the two designs, the design where the screen was attached to the beam itself was chosen as this can be modelled as a distributed load. * A rectangular block cross-section is slightly more efficient than a hollow rectangular cross-section. * An "I" cross-section is a good deal more efficient than either a solid or hollow rectangular cross-section. * A beam based on either the hollow rectangular or "I" cross-sections uses less material and will hence cost less in terms of the raw materials and will have a lower mass increasing the beam's safety For these reasons the "I" beam was chosen as the cross-section of choice. Final Design Based on the conclusions above, this report finds that the following design should be put forward to the contractor for their approval.

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