Mpadr elena pasternak slide rotation about elena pasternak slide mpa

1. Revise problem 5 from practical session wk1. The solution is provided in the practical session
solutions last week (LMS).

Do you have any questions?

selection

Example 1.8
The two-bar truss ABC shown in Figure 1.33 has pin supports at points A and C, which are 2.0m apart. Members AB and BC are steel bars, pin connected at joint B. The length of bar BC is 3.0m. A sign weighing 5.4kN is suspended from bar BC at points D and E, which are located 0.8m and 0.4m respectively from the ends of the bar.

2. Normal, Shear and Bearing

Dr Elena Pasternak Slide 5

Dr Elena Pasternak Slide 8

Problem 1.2.

Two forces are applied to the bracket BCD as shown.

c) Determine the required thickness of the bracket supports at C, knowing that the allowable bearing stress of the steel used is 300 MPa.

At the discretion of the tutor this problem may be given for homework.

4. Stress in 3D.

		0 	0	0
			6	0
			0	2

Dr Elena Pasternak Slide 15

a 11				cos(		x 1			,		x 1								cos							2		/				)				2
a 12						x 1			,		x		2		)				cos		45					2		/
a 13						x 1			,		x 3				)				cos		90					0
a	21			cos(		x 2			,						)				cos		135						cos(				
a	22				cos(		x	2		,		x		2		)				cos		45					2		/	2
a	23					x		2	,						)				cos		90			
a	23					x		2	,						)				cos		90														1	0
a 31				cos(		x 3			,		x 1				)				cos		90					0
a 32					cos(	x 3			,						)					cos		90		
a 32					cos(	x 3			,						)					cos		90												2	2
a 33						x 3			,						)				cos		0											A			1	0
a 33						x 3			,						)				cos		0														2	0
																																		0	0	1
																																		0	Slide 17

x2

22=6	x2	22=321=3	12=3 11=3

Dr Elena Pasternak	x	x3	Slide 19
Dr Elena Pasternak	3	x3	Slide 19

5. Stress transformation - Stress on inclined sections (stress on oblique planes) in 3D (multiaxial loading)

Dr Elena Pasternak Slide 21

p=10MPa, q=20MPa

x3		q

x3		x1	x3							3	2																		0
x1		x1	x3																						AA T
x1				x2								cos			x3		sin	30			1	/	2	A			
x1	1	0													0
x1	1	0													60														3
x2	0	cos					30																						3
																														2
																												0		3
x3	0	cos( 90				30		)		sin	30																	0		2
x3	0	cos( 90				30		)				1	/	2	cos		30			3		/
												1	/	2	cos		30			3		/							Slide 24

Let q= 20 MPa, p =10 MPa. Then

Dr Elena Pasternak					20		0		0			Slide 26
							17 5.		.4 33
					0				12 5.

	x2	11=-20 MPa

20 MPa

20 MPa x2 20 MPa

	x1		Slide 28

6. Stress transformation -stress on the inclined planes (oblique planes) under axial loading

Dr Elena Pasternak Slide 29

Dr Elena Pasternak Slide 30

Gere and Timoshenko (1999)

Dr Elena Pasternak Slide 34

Dr Elena Pasternak Slide 35

y	e2	x	x	y	z
		x	a11	a12	a13
25º		y	a21	a22	a23
e2		z	a31	a32	a33
e2					a33
e3	e3				Slide 36
z
Dr Elena Pasternak

=A··AT



0.906

0

0.423

0.906

Dr Elena Pasternak	z		Slide 39

x

75MPa

7. Reflection/Feedback

8. Any questions?