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Analytical Methods to Analyse Building Services

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Introduction

Unit 3 Analytical Methods Task 4 - Analytical methods to analyse building services P4a) a) Define the following terms, specifying units and equations. Include illustrative diagrams, - Stress; (Taken from http://www.en.wikipedia.org) Stress, defined as force per unit area, is a measure of the intensity of the total internal forces acting within a body across imaginary internal surfaces, as a reaction to external applied forces and body forces. The SI unit for stress is the Pascal (symbol Pa), the same as that of pressure. Since the Pascal is so small (1 N/m2), engineering quantities are usually measured in megapascals (MPa) or gigapascals (GPa). In Imperial units, stress is expressed in pounds-force per square inch (psi) or kilopounds-force per square inch (ksi). The formula to work out the force being applied to an area is; ? = F - Stress = Force A Area Tensile strength (stress) ?UTS, or SU measures the stress required to pull something such as rope, wire, or a structural beam to the point where it breaks. The tensile strength of a material is the maximum amount of tensile stress that it can be subjected to before failure. The definition of failure can vary according to material type and design methodology. This is an important concept in engineering, especially in the fields of material science, mechanical engineering and structural engineering. ...read more.

Middle

Below is a diagram of part of a roof truss. You as the structural Engineer have been asked to determine the resultant force Drawing 2 To determine the resultant force I must convert the diagram shown in drawing 2 and change it to a parallelogram, shown in drawing 3 Drawing 3 To continue with the calculation I need to find the angles I have shown this below in drawing 4. Drawing 4 So, to calculate the force on the resultant I must use the cosine law, as I now have the angles relevant to the Resultant. The cosine law is: a2 = b2 + c2 - 2bc cos A So, a2 = 82 + 52 - 2 x 8 x 5 cos 100� = 64 + 25 - ( -13.89) = 89 + 13.89 = 102.89 = V 102.89 = 10.14KN The resultant force is 10.14 KN P4b) Use the principals of calculus to solve problems appropriate to construction, civil engineering and building services engineering. a) Integrate each of the following with respect to x: .i) 6x2 - 4x + 3 ii) 1 / Vx iii) Vx3 i) When using the principals of calculus the equation looks like this; dy = 6 x 2 - 4 x 2 + 3 dx When integrated it becomes Y= 6x 3 - 4 x 2 + 3c 3 2 ii) ...read more.

Conclusion

- 3400 r -2 = 3400 r -2 = 4 ?r = 3400 = 4 ?r r2 3400 = 4 ?r x r2 3400 = 4 ?r 3 3400 = r3 4 ? To be able to continue with this calculation I must use the figures I have find through the previous formulas, so; 3400 = r 3 12.56 = 270.703 r = 3V 270.70 = 6.47 Height = 1700 ?r2 = 1700 3.14 x 6.52 = 1700 132.73 = 12.81 To be able to find the least surface I must differentiate again; da = 4 ?r + (- 3400r -2) dr = 4 ? + 3400 r-3 = 4 ? + ( 2 x 3400 r-3) = 4 ? + 6800 r-3 = 4 ? + 6800 r3 = 4x 3.14 + 6800 274.62 = 24.81 (D3c) Convergent and lateral thinking has taken place (D3d) Problems have been solved Below shows a member of a roof truss, as the structural engineer you have been asked to calculate the resultant forces Drawing 6 As with (P4c) I must turn drawing 6 into a parallelogram, illustrated in drawing 7; Drawing 7 a2 = b2 + c2 - 2 x 20 x 5 Cos 90� a2 = 202 + 102 - 2 x 20 x 5 COS 90� = 500 - 0 = 500 = V500 = 22. ...read more.

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