CIV4505: Structural Analysis Report 2 Assessment 2

Assessment 

Questions 

1. Statically indeterminate beam analysis. 

a) Calculate the BMs (bending moments) at all the joints of the beam shown in Fig.1 using the moment distribution method. The beam is subjected to an UDL of w kN/m. L1= 0.4L. Assume the support at C is pinned, and A and B are roller supports. E = 200 GPa, I = 250x106 mm4. Use the values of w and L from Table 1 based on the last digit of your student ID and proceed. At the very beginning of your solution, clearly state the values of L and w that you have used. 

b) Draw the shear force and bending diagrams for the entire beam. 

c) Calculate the BMs at all the joints of the same beam shown in Fig.1 using the slope deflection method.

d) Compare the values of BMs obtained using the two methods a) and c) and comment.

2. Statically determinate or indeterminate truss analysis by the stiffness method

a) For the truss shown in Fig 2, determine the stiffness matrices of elements 2, 3 and 4 in the in the global co-ordinate system. Assume for each member A = 0.0015 m2 and E = 200 GPa. Indicate the degrees-of freedom in all the stiffness matrices.

b) Determine the stiffness matrix of the whole truss in the global co-ordinate system. Clearly indicate the degrees-of freedom numbers in the stiffness matrix. 

c) Calculate all the nodal displacements and all the member forces of the truss. 

d) Repeat the problem using the Strand7 finite element software package. Show the truss model with loadings and boundary conditions. Display the deflected shape of the truss. Submit a hard copy from Strand7 showing the nodal displacements and member forces (highlight these in the hard copy). 

e) Present a table showing the comparisons of member forces from the stiffness method (manual calculations) and Strand7 analysis. Compare the maximum vertical deflection of the truss based on the stiffness method and Strand7 analysis. Comment on the comparisons of the values between the two.

3. Statically determinate or indeterminate beam analysis by the stiffness method

a) Determine the global stiffness matrix of the beam shown in Fig. 3. Assume supports at 1 and 3 are rollers and the support at 2 is a pinned support. Indicate the degreesof freedom in all the stiffness matrices. EI is constant. Use the values of w and L1 from Table 2 based on the last digit of your student ID. Note, L2=3L1.

b) Determine the rotations at all the nodes of the beam and reactions at the supports. Show all calculations.

c) Draw the BMD of the beam on the compression side showing the salient values. What are the maximum bending moments of the beam? Draw the deflected shape of the beam. 

d) Solve the problem using the Strand7. Assume any suitable value of EI (state the value you have used for EI). Show the model with all the nodes, element numbers and boundary conditions. Display the deflected shape and BMD. 

e) Show a table comparing the stiffness method (manual calculations) of the all the reactions and the maximum bending moment values with those of Strand7 results. Comment on the comparisons of the values between the two.

4. Statically determinate or indeterminate frame analysis by the stiffness method

a) Determine the stiffness matrix of the frame as shown in Fig. 4. Nodes 1 and 3 are fixed supports. Assume I = 300(106) mm4, A = 10(103) mm2, E = 200 GPa for each member. Indicate the degrees-of freedom in all the stiffness matrices. Use the values of L3, w and P from Table 3 based on the last digit of your student ID. Note, L4=1.8L3 (i.e. 1.8 times L3).

b) Determine all the displacement components at node 2 and all internal reactions at node 2. Show all calculations.

c) Draw the BMD of the frame on the compression side showing all the salient values. Show all calculations.

d) Repeat the problem using the Strand7. Show the model with all the nodes and element numbers and boundary conditions. Submit a hard copy from Strand7 showing all the reactions (highlight these in the hard copy). Display the bending 

Brief Summary of Assessment Requirements

This assessment focuses on advanced structural analysis techniques applied to beams, trusses, and frames. The primary objective is to test the student’s ability to analyze statically determinate and indeterminate structures using both classical analytical methods and the stiffness method, along with validation through finite element software (Strand7).

The assessment is divided into four major problem areas:

1. Statically Indeterminate Beam Analysis

   • Calculation of bending moments at joints using:
     • Moment Distribution Method
     • Slope Deflection Method
   • Construction of shear force and bending moment diagrams
   • Comparison and commentary on results obtained from both methods
2. Truss Analysis Using the Stiffness Method
   • Development of element stiffness matrices in global coordinates
   • Assembly of the global stiffness matrix
   • Calculation of nodal displacements and member forces
   • Verification using Strand7 software
   • Comparative analysis between manual and software results
3. Beam Analysis Using the Stiffness Method
   • Formation of global stiffness matrix with defined degrees of freedom
   • Determination of nodal rotations and support reactions
   • Drawing of bending moment diagram and deflected shape
   • Strand7 modeling and result comparison
4. Frame Analysis Using the Stiffness Method
   • Development of frame stiffness matrix
   • Calculation of nodal displacements and internal reactions
   • Drawing of bending moment diagrams
   • Strand7 analysis and result validation

Key Pointers to be Covered:

• Correct identification of degrees of freedom
• Accurate stiffness matrix formulation
• Clear step-by-step calculations
• Proper diagrammatic representation (SFD, BMD, deflected shapes)
• Critical comparison between analytical and software-based results
• Use of student-specific data (L, w, P) as per tables provided

Step-by-Step Approach Guided by the Academic Mentor

The academic mentor followed a systematic and structured guidance approach to ensure the student addressed each requirement effectively.

1. Understanding the Problem and Data Setup

The mentor first ensured the student clearly understood:

• Support conditions and structural behavior
• Given material properties (E, I, A)
• Student ID–based parameter selection (L, w, P)
• Importance of clearly stating assumed values at the beginning

2. Analytical Method Application

For each structure type, the mentor guided the student to:

• Identify degrees of freedom
• Establish member stiffness relationships
• Apply equilibrium and compatibility conditions
• Perform manual calculations step by step

For beam problems, classical methods (moment distribution and slope deflection) were solved first to build conceptual clarity before transitioning to the stiffness method.

3. Diagram Construction

The mentor emphasized:

• Logical derivation of shear force and bending moment values
• Correct sign conventions
• Clear marking of salient values
• Representation of compression-side bending moments and deflected shapes

4. Software Validation Using Strand7

Once manual solutions were complete:

• The mentor guided the student in modeling the structure in Strand7
• Boundary conditions, loads, and material properties were verified
• Results such as nodal displacements, member forces, BMDs, and deflected shapes were extracted
• Screenshots and hard-copy outputs were prepared as required

5. Comparison and Critical Commentary

The student was coached to:

• Tabulate manual vs software results
• Identify minor variations due to numerical approximations
• Comment on accuracy, consistency, and reliability of methods
• Draw meaningful engineering conclusions

Outcome Achieved

• Complete and well-structured solutions for all four structural systems
• Accurate stiffness matrices and displacement calculations
• Clear graphical outputs (SFDs, BMDs, deflected shapes)
• Successful validation of manual methods using Strand7
• Logical comparisons demonstrating consistency between analytical and numerical approaches

Learning Objectives Covered

Through this guided approach, the assessment successfully covered:

• Advanced structural analysis techniques
• Application of classical and matrix-based methods
• Understanding of structural behavior under loading
• Development of computational and software skills
• Engineering judgment through result comparison
• Professional presentation of calculations and diagrams

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