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ENG10003 Mechanics of Structures

Virtual Laboratory Session #1

Truss Analysis

Introduction

There are two parts in this laboratory session. 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 is to be done by watching the uploaded video and involves loading a pin-jointed
truss and measuring the forces within the structural members. These measurements will be
compared to your Part 1 calculations.

Each student is required to submit a soft copy of this working sheet due in CANVAS on 28
September, which is worth 5% of your total marks for this subject.

PART 1: Calculation of reactions and forces within members of a pin-jointed truss

For the pin-jointed truss below,

1. Calculate the reactions.
2. Calculate the forces in members BC, BD and DE by the method of joints.
3. Check your answers to the above-mentioned members by using the method of sections.

(All working for the reactions and structural members must be shown.)

Solve for:

Case 1: P = 1 N; W = 0 N
Case 2: P = 0 N; W = 1 N

Case 3: P = 1 N; W = 1 N

Student Name:

ID No:

Summary of Results for Part 1

CASE 1

Reactions RAH =______ N; RAV =______ N; RCV =______ N

Internal forces

FBC = ______ N; FBD =______ N; FDE =______ N

FAB* = ______ N; FBE* =______ N; FEA* =______ N; FCD* =______ N

*Members AB, BE, EA and CD are optional.

CASE 2

Reactions RAH =______ N; RAV =______ N; RCV =______ N
Internal forces FBC = ______ N; FBD =______ N; FDE =______ N
FAB* = ______ N; FBE* =______ N; FEA* =______ N; FCD* =______ N
*Members AB, BE, EA and CD are optional.

CASE 3

Reactions RAH =______ N; RAV =______ N; RCV =______ N
Internal forces FBC = ______ N; FBD =______ N; FDE =______ N
FAB* = ______ N; FBE* =______ N; FEA* =______ N; FCD* =______ N

*Members AB, BE, EA and CD are optional.

Note: Your full-worked solutions MUST be attached to this working sheet.

PART 2: Experiment to determine reactions and member forces in a model pin-jointed truss

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

An example of determining Reactions on a Model Truss (with load at Node B) is shown below.
.

Example Truss with Central Point Load of 118.1 gram or 0.1181 * 9.81 = 1.16 N.
The LHS vertical reaction, RAV = (170.3 – 114.5) / 1000 * 9.81 = 0.547 N.
The RHS vertical reaction, RCV = (159.6 – 100.9) / 1000 * 9.81 = 0.576 N.
Hence, the total is 1.12 N. (This is in close agreement with the value of applied load of 1.16 N)

Determining Member Forces using Simplified Photogrammetry.
Measuring the elongation or contraction in the spring of these special truss members using a
simplified photogrammetric method is a very simple way of experimentally determining their
forces (as shown below). 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. Measure distances L0
and a0 on this photo (e.g. using a ruler or the digital calliper provided of the image on your phone
if using a phone camera).

Before Application of Load

Consider the same member after application of loading. Take a close-up photo of the slot of the
member that clearly depicts the internal pointer and its position. Measure distances L1 and a1 on
this photo or the image on your phone e.g. using a ruler or the digital calliper provided.

After Application of Load

Since the actual slot length is 13.0 mm in each of the truss members, the position of the internal
pointer from the edge of the slot is in the proportion a/L of the slot length (irrespective whether
the photo is rectified or not). The elongation of the member, δm, after application of the load
becomes:

δm = 13.0 × −�
𝑎𝑎0
𝐿𝐿0
−𝑎𝑎1𝐿𝐿1� mm

You should familiarize yourself with these members and investigate the difference between how
tensile and compressive forces change the measurements.

Stiffness of the spring, Km = ___________ N/mm

Using the spring stiffness (Km) and elongation or contraction δm, the force in each member is
determined from:

Fm = (Km × δm) N

LOAD CASE 1 – MEASURED

P = ___________ gr = ___________ N

Obtain reaction forces and forces in members BC, BD and DE. Other members are optional.

Reactions RAV =______ N; RCV =______ N

Members δBC = ______ mm; δBD =______ mm; δDE =______ mm

F
=

K
m

FBC = ______ N; FBD =______ N; FDE =______ N

δAB = ______ mm; δBE =______ mm; δEA =______ mm; δCD =______ mm

FAB = ______ N; FBE =______ N; FEA =______ N; FCD =______ N

LOAD CASE 2 – MEASURED

W = ___________ gr = ___________ N

Obtain reaction forces and forces in members BC, BD and DE. Other members are optional.

Reactions RAV =______ N; RCV =______ N
Members δBC = ______ mm; δBD =______ mm; δDE =______ mm
F
=
K
m
δ

FBC = ______ N; FBD =______ N; FDE =______ N
δAB = ______ mm; δBE =______ mm; δEA =______ mm; δCD =______ mm
FAB = ______ N; FBE =______ N; FEA =______ N; FCD =______ N

Now that you have completed load cases 1 and 2 – you should be able to estimate the reactions
and relevant member forces for load case 3. Complete this on the diagram below.

Once you have estimated the reactions and member forces for each load case, you should then load
the truss and record your measurements. If your estimated reactions and member forces deviate
too much from the measured reactions and member loads – then you have probably made a mistake
and will need to go back and re-examine each load case.

LOAD CASE 3 – MEASURED

P = ___________ N (nominated earlier); W = ___________ N (nominated earlier)

Obtain reaction forces and forces in members BC, BD and DE. Other members are optional.

Reactions RAV =______ N; RCV =______ N
Members δBC = ______ mm; δBD =______ mm; δDE =______ mm
F
=
K
m

δ
FBC = ______ N; FBD =______ N; FDE =______ N

δAB = ______ mm; δBE =______ mm; δEA* =______ mm; δCD =______ mm
FAB = ______ N; FBE =______ N; FEA* =______ N; FCD =______ N

Now compare your estimated and measured actions against the calculations performed in Part 1.

Estimated from Load Cases
1 and 2 – Part 2

Hint: apply the superposition
principle.

Measured Load
from Case 3

Calculated from Load Cases 1
and 2 – Part 1

Hint: scale them up separately based on
measured P and W, then apply the

superposition principle.

FBC
FBD
FDE
FAB*
FBE*
FEA*
FCD*

*Members AB, BE, EA and CD are optional.

CONCLUSIONS:

1. By comparing the estimated actions (reactions and selected member forces) obtained from

Load Cases 1 and 2 with the actual experimental measurements from Load Case 3, please
describe and explain the findings?

2. There will be discrepancies between theoretical estimates (Part 1) and actual measurements

(Part 2). Can you think of any possible sources of errors? How can we minimise the
discrepancies?

Laboratory Session Feedback:

In this practice, rank the parts (on a scale of 1 – lowest to 5-highest) you gained most from:

1. Matching theoretical calculations to actual measured loads.
2. Learning about measurements using photogrammetry.
3. Visualising what a pin-jointed truss actually looks like and seeing how it works.
4. Overall, has this laboratory session helped you understand more about trusses?
5. Other feedback: ____________________________________________________________
__________________________________________________________________________

ENG1000

eek

Mechanics of Structures

Virtual Laboratory Session

Truss Analysis

Lab Session 1 – Truss Analysis –

ENG10003

A B C

3 5
2 6
4
7

7 Members
5 Joints

2 Supports
3 Reactions

RAH

RAV RCV

Lab Session 1 – Truss Analysis – ENG10003
3

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, B

and DE from the internal member spring displacements.

Case 1 Case 2 Case 3

Case 0

No Load Vertical Load Combined LoadsHorizontal Load

D
B
E

W
B
E
CA

D
P

CA
B

E
CA
D
B

Lab Session 1 – Truss Analysis – ENG10003
4

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
5

Vertical Reactions at A and C Case 0

No Load

WA0

A C

A
C

WA0 (gr) WC0 (gr)

WA0 (gr) WC0 (gr)
Case 0

Joint A

Lab Session 1 – Truss Analysis – ENG10003
6

Vertical Reactions at A and C Case 1 Horizontal Load

A C

WA1 (gr) WC1 (gr)

WA1 (gr)

P (gr)

Lab Session 1 – Truss Analysis – ENG10003
7

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

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

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

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

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

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

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

Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
Slide Number 8
Slide Number 9
Slide Number 10
Slide Number 11
Slide Number 12
Slide Number 13

ENG10003
MECHANICS OF STRUCTURES

SUPPLEMENT

WEEK 7 – LAB 1
TRUSS ANALYSIS

SWINBURNE UNIVERSITY OF TECHNOLOGY

ENG10003_Lab1_Supplement

VERSION 2.0. Last updated: 8 September 2020 1

Contents

Loads

………………………………………………………………………………………………………………………………………………………………………………….. 2

Reactions

…………………………………………………………………………………………………………………………………………………………………………… 3
CASE 0 – No Load ………………………………………………………………………………………………………………………………………………………… 3
CASE 1 – Horizontal Load …………………………………………………………………………………………………………………………………………. 4
CASE 2 – Vertical Load ……………………………………………………………………………………………………………………………………………….. 5
CASE 3 – Combined Loads …………………………………………………………………………………………………………………………………………. 6

Members

…………………………………………………………………………………………………………………………………………………………………………… 7
Member AE …………………………………………………………………………………………………………………………………………………………………… 7

Case 0 ………………………………………………………………………………………………………………………………………………………………………… 7
Case 1 ………………………………………………………………………………………………………………………………………………………………………… 8
Case 2 ………………………………………………………………………………………………………………………………………………………………………… 9
Case 3 ……………………………………………………………………………………………………………………………………………………………………… 10

Member AB………………………………………………………………………………………………………………………………………………………………… 11
Case 0 ……………………………………………………………………………………………………………………………………………………………………… 11
Case 1 ……………………………………………………………………………………………………………………………………………………………………… 12
Case 2 ……………………………………………………………………………………………………………………………………………………………………… 13
Case 3 ……………………………………………………………………………………………………………………………………………………………………… 14

Member BE ………………………………………………………………………………………………………………………………………………………………… 15
Case 0 ……………………………………………………………………………………………………………………………………………………………………… 15
Case 1 ……………………………………………………………………………………………………………………………………………………………………… 16
Case 2 ……………………………………………………………………………………………………………………………………………………………………… 17
Case 3 ……………………………………………………………………………………………………………………………………………………………………… 18

Member ED………………………………………………………………………………………………………………………………………………………………… 19
Case 0 ……………………………………………………………………………………………………………………………………………………………………… 19
Case 1 ……………………………………………………………………………………………………………………………………………………………………… 20
Case 2 ……………………………………………………………………………………………………………………………………………………………………… 21
Case 3 ……………………………………………………………………………………………………………………………………………………………………… 22

Member BD ……………………………………………………………………………………………………………………………………………………………….. 23
Case 0 ……………………………………………………………………………………………………………………………………………………………………… 23
Case 1 ……………………………………………………………………………………………………………………………………………………………………… 24
Case 2 ……………………………………………………………………………………………………………………………………………………………………… 25
Case 3 ……………………………………………………………………………………………………………………………………………………………………… 26

Member BC ………………………………………………………………………………………………………………………………………………………………… 27
Case 0 ……………………………………………………………………………………………………………………………………………………………………… 27
Case 1 ……………………………………………………………………………………………………………………………………………………………………… 28
Case 2 ……………………………………………………………………………………………………………………………………………………………………… 29
Case 3 ……………………………………………………………………………………………………………………………………………………………………… 30

Member CD ………………………………………………………………………………………………………………………………………………………………… 31
Case 0 ……………………………………………………………………………………………………………………………………………………………………… 31
Case 1 ……………………………………………………………………………………………………………………………………………………………………… 32
Case 2 ……………………………………………………………………………………………………………………………………………………………………… 33
Case 3 ……………………………………………………………………………………………………………………………………………………………………… 34

ENG10003_Lab1_Supplement

VERSION 2.0. Last updated: 8 September 2020 2

LOADS

Horizontal Load, P* (gr) Vertical Load, W* (gr)