Basics of Structural Analysis - Revision history

Mol: /* Introduction */

2024-01-23T07:19:46Z

Introduction

← Older revision		Revision as of 10:19, 23 January 2024
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	* <math>E</math> Young's modulus <math>\sigma = E\epsilon</math> is to be compared to <math>F= kx</math>		* <math>E</math> Young's modulus <math>\sigma = E\epsilon</math> is to be compared to <math>F= kx</math>
	* <math>\sigma</math> is the stress (force) in the material. It is defined as <math>\sigma = \frac{F}{A}</math>		* <math>\sigma</math> is the stress (force) in the material. It is defined as <math>\sigma = \frac{F}{A}</math>
			* <math>\sigma_{cr}</math> Critical stress.
			* <math>\sigma_{cr}</math>
			* <math>\sigma_{cr}</math>
			* <math>\sigma_{cr}</math>

	* <math>\epsilon</math> is the strain or deformation (displacement) in the object (perhaps in the dimension of length ratio): <math>\epsilon = \frac{\partial}{\partial X}(x-X)= F'-I</math> where <math>X</math> is the reference position of material. For a uniform bar <math>\epsilon = \frac{\Delta L}{L} = \frac{\sigma}{E} = \frac{F}{AE}</math>.		* <math>\epsilon</math> is the strain or deformation (displacement) in the object (perhaps in the dimension of length ratio): <math>\epsilon = \frac{\partial}{\partial X}(x-X)= F'-I</math> where <math>X</math> is the reference position of material. For a uniform bar <math>\epsilon = \frac{\Delta L}{L} = \frac{\sigma}{E} = \frac{F}{AE}</math>.
	* <math>\lambda</math> is the stretch ratio: <math>\lambda = \frac{L+\Delta L}{L}</math>		* <math>\lambda</math> is the stretch ratio: <math>\lambda = \frac{L+\Delta L}{L}</math>
	* <math></math>		* <math>\nu</math> Poisson ratio is a measure of deformation of material. <math>\nu = - \frac{d \epsilon_y}{d \epsilon_x}</math>
	* <math></math>		* <math></math>

Mol: /* Introduction */

2024-01-23T07:10:33Z

Introduction

← Older revision		Revision as of 10:10, 23 January 2024
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	* <math>E</math> Young's modulus <math>\sigma = E\epsilon</math> is to be compared to <math>F= kx</math>		* <math>E</math> Young's modulus <math>\sigma = E\epsilon</math> is to be compared to <math>F= kx</math>
	* <math>\sigma</math> is the stress (force) in the material. It is defined as <math>\sigma = \frac{F}{A}</math>		* <math>\sigma</math> is the stress (force) in the material. It is defined as <math>\sigma = \frac{F}{A}</math>
	* <math>\epsilon</math> is the strain or deformation (displacement) in the object (perhaps in the dimension of length ratio): <math>\epsilon = \frac{\partial}{\partial X}(x-X)= F'-I</math> where <math>X</math> is the reference position of material. For a uniform bar <math>\epsilon = \frac{\Delta L}{L} = \frac{\sigma}{E} = \frac{F}{AE}</math>		* <math>\epsilon</math> is the strain or deformation (displacement) in the object (perhaps in the dimension of length ratio): <math>\epsilon = \frac{\partial}{\partial X}(x-X)= F'-I</math> where <math>X</math> is the reference position of material. For a uniform bar <math>\epsilon = \frac{\Delta L}{L} = \frac{\sigma}{E} = \frac{F}{AE}</math>.
	* <math></math>		* <math>\lambda</math> is the stretch ratio: <math>\lambda = \frac{L+\Delta L}{L}</math>
	* <math></math>		* <math></math>
	* <math></math>		* <math></math>

Mol: /* Introduction */

2024-01-23T07:07:40Z

Introduction

← Older revision		Revision as of 10:07, 23 January 2024
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	Structural analysis using about high school level physics and maths.		Structural analysis using about high school level physics and maths.

	~~Aim~~ to ~~calculate fiberglass cansat structure~~		The terms used
			* <math>E</math> Young's modulus <math>\sigma = E\epsilon</math> is to be compared to <math>F= kx</math>
			* <math>\sigma</math> is the stress (force) in the material. It is defined as <math>\sigma = \frac{F}{A}</math>
			* <math>\epsilon</math> is the strain or deformation (displacement) in the object (perhaps in the dimension of length ratio): <math>\epsilon = \frac{\partial}{\partial X}(x-X)= F'-I</math> where <math>X</math> is the reference position of material. For a uniform bar <math>\epsilon = \frac{\Delta L}{L} = \frac{\sigma}{E} = \frac{F}{AE}</math>
			* <math></math>
			* <math></math>
			* <math></math>

	== Basic theory ==		== Basic theory ==

Mol: Mol moved page Structural analysis of a Cansat to Basics of Structural Analysis: Too much text

2024-01-23T06:57:04Z

Mol moved page Structural analysis of a Cansat to Basics of Structural Analysis: Too much text

← Older revision	Revision as of 09:57, 23 January 2024
(No difference)

Mol: /* Cylindrical Pipe */

2024-01-21T17:11:05Z

Cylindrical Pipe

← Older revision		Revision as of 20:11, 21 January 2024
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	== Cylindrical Pipe ==		== Cylindrical Pipe ==

			[[File:AxialStress.svg\|thumb\|Axial stress]]

	Cylinder stress		Cylinder stress

Mol: /* Axial stress */

2024-01-21T17:04:23Z

Axial stress

← Older revision		Revision as of 20:04, 21 January 2024
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	'''External pressure'''		'''External pressure'''

			The critical stress is <math>\sigma_{cr} = \frac{F}t = \frac{RE}{S(1-\nu^2)}</math>, where <math>E</math> is the Young's modulus, <math>\nu</math> is the Poisson ratio, <math>R</math> is the radius of the shell and . . .[Not ok. . . , see https://core.ac.uk/download/pdf/10851171.pdf page 28. ]

	'''Internal pressure'''		'''Internal pressure'''

Mol: /* Axial stress */

2024-01-21T16:59:05Z

Axial stress

← Older revision		Revision as of 19:59, 21 January 2024
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	The force <math>p_iA_i</math> from the internal pressure is equilibrated by the wall stress <math>\sigma_a A_a = \sigma_a (A_o - A_i)</math> where <math>A_i</math> is internal area and <math>A_o</math> is the outer area.		The force <math>p_iA_i</math> from the internal pressure is equilibrated by the wall stress <math>\sigma_a A_a = \sigma_a (A_o - A_i)</math> where <math>A_i</math> is internal area and <math>A_o</math> is the outer area.

	The force on the direction of axis (from center to the loop) due to the pressure is		The force on the direction of axis (from center to the loop) due to the internal pressure is
	<math>		<math>
	F = \int_0^r 2 p \pi r dr = 2 p \pi \frac{r^2}{2} = p \pi \frac{D^2}{4}		F = \int_0^r 2 p \pi r dr = 2 p \pi \frac{r^2}{2} = p \pi \frac{D^2}{4}

Mol: /* Axial stress */

2024-01-21T16:51:09Z

Axial stress

← Older revision		Revision as of 19:51, 21 January 2024
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	=== Axial stress ===		=== Axial stress ===

	The axial stress is uniform across the cylinder wall. The stress is found by equilibrium calculations (see below). See the difference between external and internal pressure. ~~We have external~~ pressure.		The axial stress is uniform across the cylinder wall. The stress is found by equilibrium calculations (see below). See the difference between external and internal pressure.

			'''External pressure'''



			'''Internal pressure'''

			The force <math>p_iA_i</math> from the internal pressure is equilibrated by the wall stress <math>\sigma_a A_a = \sigma_a (A_o - A_i)</math> where <math>A_i</math> is internal area and <math>A_o</math> is the outer area.

	The force on the direction of axis (from center to the loop) due to the pressure is		The force on the direction of axis (from center to the loop) due to the pressure is

Mol: /* Axial stress */

2024-01-21T15:08:16Z

Axial stress

← Older revision		Revision as of 18:08, 21 January 2024
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	=== Axial stress ===		=== Axial stress ===

	The axial stress is uniform across the cylinder wall. The stress is found by equilibrium calculations (see below).		The axial stress is uniform across the cylinder wall. The stress is found by equilibrium calculations (see below). See the difference between external and internal pressure. We have external pressure.

	The force on the direction of axis (from center to the loop) due to the pressure is		The force on the direction of axis (from center to the loop) due to the pressure is

Mol: /* Axial stress */

2024-01-21T15:07:35Z

Axial stress

← Older revision		Revision as of 18:07, 21 January 2024
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	=== Axial stress ===		=== Axial stress ===

			The axial stress is uniform across the cylinder wall. The stress is found by equilibrium calculations (see below).

	The force on the direction of axis (from center to the loop) due to the pressure is		The force on the direction of axis (from center to the loop) due to the pressure is