lab report engeenring

ENG10003

Week 7

Mechanics of Structures

Virtual Laboratory Session 1 Truss Analysis

Lab Session 1 – Truss Analysis – ENG10003

2

1 3 5

2 6

4

7

A B

C

DE

1

A B C

DE

3 5

2 6

4

7

7 Members 5 Joints

2 Supports 3 Reactions

RAH

RAV RCV

Lab Session 1 – Truss Analysis – ENG10003

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In the laboratory session, you will be investigating the truss shown for different load cases. For each load case, you will need to determine the reactions at A and C (with the help of digital scales), and the internal forces in members BC, BD and DE from the internal member spring displacements.

Case 1 Case 2 Case 3Case 0 No Load Vertical Load Combined LoadsHorizontal Load

P

W

D

B

E

CA

W

B

E

CA

D P

DE

CA B

E

CA

D

B

Lab Session 1 – Truss Analysis – ENG10003

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The lab reports include

two parts

Part 1 is to be completed in your own time and involves the calculation of reactions and

member forces by the method of joints and method of sections.

Part 2 will be explained in this video through the next slides.

Theoretical Part Experimental Part

In the end, these results need to be compared with each other.

Lab Session 1 – Truss Analysis – ENG10003

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Vertical Reactions at A and C Case 0 No Load

WA0

A CA C

WA0 (gr) WC0 (gr)

WA0 (gr) WC0 (gr)

Case 0

Joint A

Lab Session 1 – Truss Analysis – ENG10003

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Vertical Reactions at A and C Case 1 Horizontal Load

A C A C

WA1 (gr) WC1 (gr)

WA1 (gr)

P

P (gr)

Lab Session 1 – Truss Analysis – ENG10003

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Vertical Reactions at A and C Case 2 Vertical Load

A C A C

WA2 (gr) WC2 (gr)

WA2 (gr) WC2 (gr)

W

W (gr)

Lab Session 1 – Truss Analysis – ENG10003 – 1S2020

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Vertical Reactions at A and C Case 3 Combined Loads

A C

A C

WA3 (gr) WC3(gr)

WA3 (gr) WC3 (gr)

P

W

Lab Session 1 – Truss Analysis – ENG10003

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Summary and conclusions Case 0

(No Load) Case 1

(Horizontal Load, P) Case 2

(Vertical Load, W) Case 3

(Combined Loads, P+W) Weight at A WA0 WA1 WA2 WA3 Vertical Reaction at A N/A RAV1 = (WA1 – WA0) RAV2 = (WA2 – WA0) RAV3 = (WA3 – WA0)

Vertical Reactions at A and C

Weight at C WC0 WC1 WC2 WC3 Vertical Reaction at C N/A RCV1 = (WC1 – WC0) RCV2 = (WC2 – WC0) RCV3 = (WC3 – WC0)

3 Cases 6 Vertical Reactions, two for each case

Lab Session 1 – Truss Analysis – ENG10003

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1

Each truss member has a spring inside that deforms a small amount when subjected to load. Consider a member before application of loading. Take a close- up photo of the slot of the member, clearly depicting the internal pointer and its position.

Internal Forces in Members

Lab Session 1 – Truss Analysis – ENG10003

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No Load

In Tension In Compression

The deflection of the member can be determined by:

𝛅𝛅𝐦𝐦 = 𝟏𝟏𝟏𝟏 × 𝐚𝐚𝟏𝟏 𝐋𝐋𝟏𝟏

− 𝐚𝐚𝟎𝟎 𝐋𝐋𝟎𝟎

The actual slot length

Elongation Contraction

Internal Forces in Members

Lab Session 1 – Truss Analysis – ENG10003

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𝐅𝐅𝐦𝐦 = 𝐤𝐤𝐦𝐦 × 𝛅𝛅𝐦𝐦

The internal force of each member can be calculated by

where km is the spring stiffness and 𝛅𝛅𝐦𝐦 is deflection of the member

𝛅𝛅𝐦𝐦 = 𝟏𝟏𝟏𝟏 × 𝐚𝐚𝟏𝟏 𝐋𝐋𝟏𝟏

− 𝐚𝐚𝟎𝟎 𝐋𝐋𝟎𝟎

𝐤𝐤𝐦𝐦 = 𝟎𝟎. 𝟖𝟖𝟖𝟖 N/mm Suggested by the manufacturer

Internal Forces in Members

No Load Combined LoadsVertical Load

Lab Session 1 – Truss Analysis – ENG10003

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All required photos for the determination of the ratios ⁄𝐚𝐚𝐢𝐢 𝐋𝐋𝐢𝐢 (before and after applying loads – cases 0-3) will be given in a separate file for all required members.

Sample Calculation – Member AE Case 0 Case 2 Case 3Horizontal LoadCase 1

Photo (i) Photo (ii) Photo (iii) Photo (iv)

𝛅𝛅𝐀𝐀𝐀𝐀𝟏𝟏 = 𝟏𝟏𝟏𝟏 × 𝐚𝐚𝟏𝟏 𝐋𝐋𝟏𝟏

− 𝐚𝐚𝟎𝟎 𝐋𝐋𝟎𝟎

𝐅𝐅𝐀𝐀𝐀𝐀𝟏𝟏 = 𝟎𝟎. 𝟖𝟖𝟖𝟖 × 𝛅𝛅𝐀𝐀𝐀𝐀𝟏𝟏

𝛅𝛅𝐀𝐀𝐀𝐀𝟐𝟐 = 𝟏𝟏𝟏𝟏 × 𝐚𝐚𝟐𝟐 𝐋𝐋𝟐𝟐

− 𝐚𝐚𝟎𝟎 𝐋𝐋𝟎𝟎

𝐅𝐅𝐀𝐀𝐀𝐀𝟐𝟐 = 𝟎𝟎. 𝟖𝟖𝟖𝟖 × 𝛅𝛅𝐀𝐀𝐀𝐀𝟐𝟐

𝛅𝛅𝐀𝐀𝐀𝐀𝟏𝟏 = 𝟏𝟏𝟏𝟏 × 𝐚𝐚𝟏𝟏 𝐋𝐋𝟏𝟏

− 𝐚𝐚𝟎𝟎 𝐋𝐋𝟎𝟎

𝐅𝐅𝐀𝐀𝐀𝐀𝟏𝟏 = 𝟎𝟎. 𝟖𝟖𝟖𝟖 × 𝛅𝛅𝐀𝐀𝐀𝐀𝟏𝟏