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DEPARTMENT OF CIVIL
ENGINEERING

STRUCTURAL ANALYSIS-II LAB MANUAL

HOD SIGNATURE

LAB INCHARGE

EXPERIMENT NO
...

2

………
...
a
...
a
...

2

Central upward deflection, y = w
...
L /
8EI Where,
a = length of overhang on each side
W = load applied at the free ends L
= main span
E = modulus of elasticity of the material of the
beam I = moment of inertia of cross section of the
2

beam EI = w
...
L / 8y
3

It is known that, EI for beam = E X bd /12
Where, b = width of beam
d = depth of beam

Procedure: i) Find b and d of the beam and calculate the theoretical value of EI by Eq
...

ii) Measure the main span and overhang span of the beam with a scale
...

iv) Repeat the above steps for different loads
...
No
...
( 3 )

EI from
Eq ( 2 )

4

Calculation: - Average values of EI from observation = ……cm
4
Average values of EI from calculation = ……
...


Precaution : - Measure the center deflection y very accurately
...

Loading should be within the elastic limit of the materials
...
2
Aim: - To verify clerk Maxwell’s reciprocal theorem
Apparatus: - Clerk Maxwell’s Reciprocal Theorem apparatus, Weight’s, Hanger, Dial
Gauge, Scale, Verniar caliper
...

Procedure: i) Apply a load either at the centre of the simply supported span or at the free end of the
beam, the deflected form can be obtained
...


iii) Now move a load along the beam at certain distance and for each positions of the
load, the deflection of the point was noted where the load was applied in step1
...

Plot the graph between deflection as ordinate and position of point on abssica the plot for
graph drawn in step2 and 3
...


Observation Table:Distance
from the
pinned
end

Load at central point/
cantilever end

Beam
unloaded
Dial gauge
reading
(mm)2

Beam
loaded
Dial
Gauge
reading
(mm)3

Deflection
of various
points
(mm) 2-3
Beam
unloaded
Dial gauge
reading
(mm)5

Load moving along
Beam

Beam
unloaded
Dial gauge
reading
(mm)5

Deflection
of various
points
(mm) 5-6

Beam
loaded
Dial gauge
reading
(mm)6

Result : - The Maxwell reciprocal theorem is verified experimentally and analytically
...

ii) Perform the experiment at a location, which is away from any
iii) Avoid external disturbance
...


EXPERIMENT NO
...


Apparatus: - Portal Frame Apparatus, Weight’s, Hanger, Dial Gauge, Scale,
Verniar caliper
...
Determinate structures can be analysed additional conditions to solve
...


To know the behavior of any frame it is advisable to know its different deflected shapes
under different loading condition, which can be obtained by vertical work energy method
analytically
...
Clearance
requirements usually lead to the use of statically indeterminate structure layout for
portals, and approximate solutions are often used in their analysis
...
The legs are hinged at their base and rigidly connected to
the cross girder at the top
...
Solution of this type of structure based on elastic
considerations, show that the total horizontal shear on the portal will be divided almost
equally between the two legs; it will therefore be assumed that the horizontal reactions
2

for the two legs are equal to each other and therefore equal to P/2
...
The vertical reaction on the right leg can be
obtained by taking moment about the hinge at the base of the left leg
...
Once
the reactions are known, the diagrams of bending moment and shear are easily computed,
leading to values for bending moment as given in fig (b)
...

Consider now portal similar in some ways to of fig
...
As when the legs were hinged at their base, it will
again be assumed that the horizontal reaction for the two legs are equal and hence equal
to P/2
...
These are points of inflection, where the bending moment is changing sign and
hence has zero value
...

ii) Select the point where loading is to be applied (first horizontal than vertical separately)
...

iv) Fix the dial gauge and adjust them to zero on one of the leg at various points and
measure the vertical distance from the end of these points
...

vi) Note down the dial gauge readings
vii) Unload the frame and shift the dial gauge to another leg and repeat the above (4), (5)
...

viii) Again unload the frame and shift the dial gauge to the beam of the frame and
repeated (4), (5)
...

ix) Tabulate the observed reading and sketch the deflected shape for the portal frame on
the graph sheet
...


Observation Table:Points on AC

Distance of
Point from C

Table: - 1
Dial gauge reading
Initial

Deflections
( mm )

Final

Table: - 2
Points on AB

Distance of
Point from A

Dial gauge reading
Initial

Final

Deflections
( mm )

Table: - 3
Points on BD

Distance of
Point from D

Dial gauge reading
Initial

Deflections
( mm )

Final

Sample Calculation: - 1) Portal frame with end
conditions = 2) Loading point x on
AC/AB/BD
Load applied = kg
Result : - The horizontal displacement obtained theoretically and experimentally
is nearly same,
Precaution : - Apply the load without jerk
...


EXPERIMENT NO
...

Apparatus: - Strain gauge Indicator, weights, hanger, scale, verniar caliper
...
The bending moment at a section tends to deflect the
beam & internal stresses tend to resist its bending
...

Following are the assumpsions in theory of simple bending
...
The material of beam is perfectly homogeneous and isotropic (i
...
have same
elastic properties in all directions
...
The beam material is stressed to its elastic limits and thus follows Hook’s
law
...
The transverse section which are plane before bending remains plane after
bending also
...
The value of young’s modulus of elasticity ‘E’ is same in tension and
compression
...

f = (M/I) y
Where, M= moment at considered section
...
I = Moment of inertia at that section
...

fmax = maximum stress at the farthest fiber i
...
at ymax from neutral
axis
...
It incorporates
basic bridge balancing network, internal dummy arms, an amplifier and a digital display
to indicate strain value
...
This results in an overall change of resistance due to change in both the
dimensions
...

Strain can be calculated analytically at the section by using Hook’s law
...
It basically incorporates basic
bridge balancing network, internal dummy arms, amplifier & digital display to indicate
strain value
...
Four -Arm Bridge requires four strain gauge and will display the strain value four
times of actual
...

ii) Connect the digital indicator to 230(+/- 10%) colts 50 Hz single phase A
...
power
supply and switch ‘ON’ the apparatus
...

iv) Push the ‘GF READ’ switch and adjust the gauge factor to that of the strain gauge
used (generally 2
...

Observation: - 1) Width of the beam model, B (cm)
2) Depth of the beam model, D (cm)
3) Span of the beam, L (cm)
4) Moment of inertia of beam, I
Ymax = D/2
5) Modulus of elasticity of beam material, E

=
=
=
=
=
=

Observation Table:S
...

Load applied on the hanger P (kg)
Moment at the mid span section (kg cm) = PL/4
f max= (M/I) Ymax
Theoretical Strain Ø = f max
E
Observed strain on the display
Result : - From observation table, it is seen that, the theoretical and observed value of

DEPARTMENT OF CIVIL ENGINEERING RCET, RAIPUR

12

STRUCTURAL ANALYSIS-II LAB MANUAL
strain is same
...

The order of some of these steps is not critical; however, all step should be completed before execution
of the the analysis
...
Charles Camp
...

Assume all members are pin connected
...
4 you should see the following interface window:

DEPARTMENT OF CIVIL ENGINEERING RCET, RAIPUR

14

STRUCTURAL ANALYSIS-II LAB MANUAL

Step 1: Set Problem Dimensions On the bottom on the interface window, set
the desired units for the problem using the
pull-down menu
...


Step 2: Grid Spacing - Determine the appropriate number of grid line and grid spacing to locate the
joints of the truss
...
To create a new problem, select
New Model under the File menu
...


Remember, that SAP2000 assumes that
your two-dimensional structure resides in
the x-z plane
...
For the truss shown above, the
the grid spacing in the x and z-directions is
20 feet
...

No y-direction grid line are necessary for
this problem
...

By default SAP2000 show two views of
your problem, typically a 3-D view and an
x-y plane view
...


DEPARTMENT OF CIVIL ENGINEERING RCET, RAIPUR

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STRUCTURAL ANALYSIS-II LAB MANUAL

Step 3: Locate Truss Joints - To define the joint locations, select the Draw Special Joint button
on the lower tool bar
...
For this problem the joint
locations are shown below:

DEPARTMENT OF CIVIL ENGINEERING RCET, RAIPUR

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STRUCTURAL ANALYSIS-II LAB MANUAL

Step 4: Draw Frame Elements - To define each frame element, select the Draw Frame Element
button
on the lower tool bar
...
To end a series of element definitions, simply double-click
on the final joint
...
A yellow "X" should appear at the joint to
indicate that it is currently selected
...


DEPARTMENT OF CIVIL ENGINEERING RCET, RAIPUR

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STRUCTURAL ANALYSIS-II LAB MANUAL
The Joint Restraints menu will appear as shown on the
right
...
When
working on two-dimensional structures, the Fast
Restraints button may be used for most problems
...

In the truss example, select the lower-left hand joint with
the pointer (an "X" should appear at the joint) and then
click on the

Fast Restraints button
...


Next, select the lower right-hand joint with the pointer and
click on the

Fast Restraints button
...


and click

After the supports have been defined the truss problem should appear in the SAP2000 interface window
as follows:

DEPARTMENT OF CIVIL ENGINEERING RCET, RAIPUR

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STRUCTURAL ANALYSIS-II LAB MANUAL

Step 6: Apply Forces at Joints - To apply forces at a joint, select the joint with the pointer and
click on the Assign Joint Loadings button


...
Remember that
the truss was modeled in the in the
x-z plane, therefore the forces are
acting in the negative z-direction
...
0 in the Forces Global Z
input field and click OK
...


DEPARTMENT OF CIVIL ENGINEERING RCET, RAIPUR

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STRUCTURAL ANALYSIS-II LAB MANUAL

Step 7: Release Internal Moments at Joints - SAP2000 assumes that all structures are
frames
...
To ensure that every joint in the structure is pin connected, select all the members by
clicking the Select All button on the bottom tool bar
...


DEPARTMENT OF CIVIL ENGINEERING RCET, RAIPUR

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STRUCTURAL ANALYSIS-II LAB MANUAL

In this example, the structure is a truss,
which by definition has no moment capacity
at each joint
...
Torsion can only be
released at one end of the element,
whereas, the other moment must be
released at both the Start and End of the
element
...
In our truss analysis, we assume that each element is weightless
...
The Define Materials window will appear as shown below:
On this menu you can change the
properties of materials
...

The Material Property Data window will
appear
...
Click OK to return to the Define
Materials window and than click OK again
...
For this example problem, the default values for the Mass per unit Volume, Modulus of
elasticity, Poisson's ratio, and the Coeff of thermal expansion can be used
...


Step 9: Define Frame Sections - To define the cross-section properties of a structural element
click on the Define menu located along the top the SAP2000 interface window and then click on Frame
Sections
...
To change the properties of the frame section click on the on
the Modify/Show Material button
...


DEPARTMENT OF CIVIL ENGINEERING RCET, RAIPUR

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STRUCTURAL ANALYSIS-II LAB MANUAL

To the material of this frame section click on the Material pull-down menu and select our weightless
material OTHER
...
If
you are interested in computing deflections in the truss, then you must define the Depth (t3) and Width
(t2) of the cross-section
...


Step 10: Assign Frame Sections - To assign the cross-section properties of a structural element,
select the element with the pointer and click on the Assign menu located along the top the SAP2000
interface window and then click on Frame Sections
...
The Frame Section name will
appear next to each element selected
...
To limit analysis to variables in the x-z plane click on the Analyze menu located
along the top the SAP2000 interface window and then click on Set Options
...
The truss
structure is now ready for analysis
...


If the analysis is successful, the Analysis Complete window will appear and report the the analysis is
complete
...


DEPARTMENT OF CIVIL ENGINEERING RCET, RAIPUR

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STRUCTURAL ANALYSIS-II LAB MANUAL
If the window reports that the analysis is incomplete, make sure that the moments have been released
and that the analysis options have been set correctly
...
The Member

DEPARTMENT OF CIVIL ENGINEERING RCET, RAIPUR

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STRUCTURAL ANALYSIS-II LAB MANUAL
The default values will display the Axial Forces
using the Fill Diagram
...


Another way to display force information is to
unclick Fill Diagram and click on Show Values
on Diagram
...


DEPARTMENT OF CIVIL ENGINEERING RCET, RAIPUR

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STRUCTURAL ANALYSIS-II LAB MANUAL

To print the results to a file click on the File menu and select Print Output Tables and click the Print to
File box
...
The default location for the file is the
same directory as the problem files
...

In order to correlation the results printed in the output file to frame elements in the structure, the frame
labels turned on and printed out
...
Next, click on the Set Elements button
Frame section of the menu click on Labels
...

The results of the truss analysis presented in the output file are listed by frame element number
...
For truss
analysis there are no bending moments and shear forces
...


DEPARTMENT OF CIVIL ENGINEERING RCET, RAIPUR

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STRUCTURAL ANALYSIS-II LAB MANUAL

DEPARTMENT OF CIVIL ENGINEERING RCET, RAIPUR

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