Structural Analysis For Civil Engineering

Task 1

Structural engineering theory is based upon the applied physical laws and empirical knowledge of the structural performance of different materials and geometries. Structural engineering design utilizes a number of simple structural elements to build complex structural systems. Structural engineers are responsible for making creative and efficient use of funds, structural elements and materials to achieve these goals

Q1.1) Discuss equilibrium and compatibility requirements for structures.

Q1.2) Determine the stress/ strain relationship of an axially loaded system and define the following terms;

Yield Strength

Limit of Proportionality

Young’s modulus

Elastic and plastic regions

Task 2

Statically determinacy is a term used in structural mechanics to describe a structure where force and moment equilibrium conditions alone can be utilized to calculate internal member actions. Descriptively, a statically determinate structure can be defined as a structure where, if it is possible to find internal actions in equilibrium with external loads, those internal actions are unique.

Q2.1) Evaluate statically determinacy and kinematical indeterminacy of the following structures using the method described below.
Classify if the structure is stable or unstable and if unstable, the reason why. If the structure is stable, indicate if determinate or indeterminate and if indeterminate the degree of indeterminacy.

Q2.2) Use the method of virtual work and analyse the vertical deflection of joint B in following complex truss form. The distance between each bay is 8 ft and for each steel member A= 1.5 in2 , E= 29(103) ksi.

Q2.3) Analyze the following structural system using influence line method.

The beam is subjected to a uniform dead load of 1.2 KN/m and a single live load of 40 KN. Determine:

a) The maximum moment created by these loads at C,

b) The maximum positive shear at C.

Assume support A is a pin and B is a roller.

Task 3

The relationship between the stress and strain that a particular material displays is known as that particular material's stress–strain curve. It is unique for each material and is found by recording the amount of deformation (strain) at distinct intervals of tensile or compressive loading (stress). These curves reveal many of the properties of a material (including data to establish the Modulus of Elasticity, E).

Q3.1) Following table shows the results of a tensile test of a 0.505 inch diameter aluminium bar. Initial length of the bar is 2 inches.

Load/(lb)   Change in length (in)
 0                   0.0
1000              0.001
3000              0.003
5000              0.005
7000              0.007
7500              0.030
7900              0.080
8000 (maximum) 0.120
7950              0.160
7600 (fracture) 0.205

i) Evaluate Stress and strain parameters for the above structural element

ii) Determine the Modulus of elasticity of the given structural element by plotting stress- strain diagram

Q3.2) What is shear flow and shear centre in beams.

A 12 in. by 5 in. British Standard Beam shown in following figure is subjected to a Shearing Force of 10 tons. Calculate the Shear Stresses
at the Neutral Axis and at the top of the Web.

Shear stress,

I = 220 in4, Web thickness = 0.35 inch and Flange thickness = 0.55 inch, z = 0.35

Q3.3) A simple beam AB with span length L= 3.5 m carries a uniform load of intensity q= 6.4 KN/m. (See the figure below). Determine the maximum bending stress σ max due to the load q if the beam has a rectangular cross section with width b=140 mm and height h=240mm.

Task 4

Q4.1) Construct the shear force diagram (S.F.D.) and bending moment diagram (B.M.D.) for the structure ABC which is loaded as shown in
Figure below. Note that BC is a cantilevered part of the structure. Calculate all the support reactions and internal forces at specified
locations on the S.F.D. and B.M.D., and also indicate the sign conventions used. Calculate the deformation (deflection) at C.

Take E = 200 GPa and I = 100 x 106 mm4

Q4.2) The statically determinant beam ABC is loaded as shown in Figure below. Determine the deflection at B for using direct integration
method.

Q4.3) a) Calculate the internal forces, support reactions and vertical deformation of joint B in following structural frame using method of
virtual work. Each steel member has a cross sectional area of 300 mm2 and E= 200 GPa.

b) Calculate the internal forces, support reactions and horizontal deformation of joint B of following structural frame using method of virtual work. Each steel member has a cross sectional area of 2 in2 and E= 29 (103 ) ksi

Q4.4) Develop a structural system using any software available and determine deflection of 3D frame.

M 3 Criteria

Should use range of methods of presentation and correct technical language throughout the report.

D 2 Criteria

Will be assessed by manage and organize the activities in assignment within the given time frame. Late submissions are not considered for D 2 criteria