Jianhu TU10 Stress transformation PDF

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By Jianhu (Chris) Shen Email: [email protected] Phone: 99250421 Office: 10.12.03.01 (city) 251.2.65 (Bundoora)

Mode of delivery and consultation  Tutorials –Practise by solving problems  Brief review on lecture notes to be used in tutorial  Feedback and comments on your learning progress and

assignments  Demonstrate the solution process for tutorial problems  Practise time and answer questions for tutorial problems  My consultations Time Wednesday: 1:30 PM to 4:30 PM Other time, please confirm available with email: [email protected]

Learning Progress for Structural Analysis Stress Transformation

DD/F

Shear Stress on Beams

Constitutive Eq

Bending Stress-Normal

Safety of an Structure

BMD/F; SFD/F; Internal forces N, Q, M

Strength

Equilibrium Eq

Slope/Deflection Equations

Rigidity

Stress

Stability

Deflection

Double integration method

Statics-FBD Section properties

Capacity

Reliability Serviceability

Materials, Geometries, Sections, Applied Load

Update on satisfactory progress on your Video Project  Select a simple structure/a part of a       

structure Approximate the selected structure to statically determinate structure Simplify geometry, section, loads, supports etc Section properties SFD/BMD; Bending stress Deflection Shear stress Principle stresses, failure planes

Deliveries: Task 1-Photograph with Related Info Due: 11th August

Task 2- Interim Report Due: 17th September Extended to: 24th September

Task 3 -Final Report and Video Presentation Due: 20th October

Update and assistance on Cardboard Project 

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: Signature for No. Get a profile shape (e.g. a triangle) including dimensions and equations from their tutors; size Due: 24th August not to exceed 500 mm in any direction. -66 students were recorded Locate centroids and CG and calculate MoI for the shape. Manufactured Profile Bring the cardboard to class room (10.12.16) Due: 13th September and demonstrate the CG on a ruler to get Extended to: 17th September feedback and comments (29 August 2018-17 September 2018) Submit all the calculations as a separate report Online submission of detailed on Canvas. Due date: 24 September 2018 calculation Due: 24th September Extended to: 1 October

Brief review on lecture notes 

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Stress transformation-planar -Stress state at one point on structure -Sign conventions -Stress components in different coordinate system with the same origin -Relation between those components Principal stresses -Maximum normal stress -Maximum shear stress Application of stress transformation

Purpose of stress transformation

We noticed that the direction of the crack development during failure are different for different type of load!! From bending theory: x

Mz y Ix

y

0

xy

VQ Ib

x'

?

y

?

x'y'

?

Stress components in different coordinate system y y' x O

Note: for beam

x'

Stress state at one point on structurecomponent in different planes Bending stress

Shear stress

All stress components for 3D and planar

Sign conventions for stress transformation

Stress components in different coordinate system y y’ x O

x’

Planar stress transformation

Mathematical representation of stress transformation

Mohr’s Circle

Graphical representation of stress transformation http://www.ijee.ie/OnlinePapers/Interactive/Philpot/ mohr_learning_tool.htm

In-plane principal stresses Maximum normal stress

Maximum shear stress

Application of stress transformation

Explain orientation of crack

Explain failure plane

Check grain strength for wood

Design welding for pressure vessels

Reminding on CES survey 1. An Email from the RMIT Student Feedback Team sent to your RMIT student email account 2. Survey Services website https://surveys.rmit.edu.au/Blue/ 3. myRMIT - under ‘Launch Application’ click on ‘Student Survey’ Comments and Feedback: Including all information relating to your learning • Your learning progress • Your expect progress on projects • Feedback and assistance on your project

Tutorial problem 1 - simple

18

Solution-P1-1 y'

y x x'

19

Tutorial problem 2 – more complex

20

Solution-P2-1 Stress state:

Principal stresses-normal stress

Solution-P2-2 Principal stresses-shear stress:

Average stress:

Solution-P2-3

Example 3-application example

24

Solution-P3-1 Work out the stress state in structural coordinate system

y x

1. Section Properties- centroid (symmetric) and second moment of inertia

2. Solve reaction forces 3. Solve internal forces at A using this FBD: We have: V= 6.857kN; M= 13.714 kN•m

4. Solve normal stress at A: 25

Solution-P3-2 5. Solve shear stress at A

Solution-P3-3 4. The stress state at A

y ɵ=115º

x

Solution-P3-4 y ɵ=115º

x

28

Solution-in class-revised 4. The stress state at A

y

x ɵ=-(90º-25º) =-65º

Solution-P3-4 y

x

30...