Matrix analysis method- Consider the following structural system: Structural analysis 2, Report, UOG, Singapore

Objectives:

Understand understanding of structural behaviour, Understand the differences in numerical, analytical results.

Part A: shown in Figure 1.

Use the Matrix analysis method to anal

 Matrix analysis method

Consider the following structural systemyse the structural response of the portal frame.

E=4500ksi, I=3500in4,  Possion Ratio=0.1 and Area=180 in2 .

a) Determine slope and vertical deflection at point “B”
b) Find reactions and draw BMD, SFD for the Frame Structure.

Part B: Structural behaviour

1) Use Matrix analysis method and STAAD. PRO to determine internal force diagrams (bending moments, shear and axial forces), reaction forces and sway (horizontal displacement of beam) of the following four systems:

B.1 uniform frame and offset load (Figure 2)
B.2 nonuniform frame and offset load (Figure 3)
B.3 nonuniform frame and centric load (Figure 4)
B.4 uniform frame and centric load (Figure 5).

Sectional properties 1: Solid rectangular cross-section with a depth of 2 mm and an out of plane thickness of 15 mm (Calculate the corresponding A1 and I1).

Sectional properties 2: Solid rectangular cross-section with a depth of 1.5 mm and an out of plane thickness of 15 mm (Calculate the corresponding A2 and I2).
Load: Force F = 4.9 N
Material properties:
Young’s modulus E = 100,000 N/mm2

2) Discuss differences in internal force distributions (axial force, shear force and bending moment diagrams) and reaction forces for the systems B.1 to B.4

3) Discuss how the sway of the frame (sway is the horizontal displacement of the horizontal beam) is influence by position of the load and the nonuniform properties of the frame.

4) Investigate the importance of the axial stiffness on the STAAD.PRO results for the system with the largest sway. Would it acceptable to assume that the members are inextensible?

5) Summarise the key results in the form of all reactions and the sway for all 4
systems in a table