Structural Analysis

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Submitted By kasungunarathna
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Structural Analysis and Modeling
Assignment – 1 2013
Answer all questions. 1. When the deflections of a statically determinant beam are calculated using singularity functions, it is necessary to know the values of 2 boundary conditions. For each of the beams below, what are the boundary conditions?

2. Calculate the reactions and draw the SFD and BMD for the cantilever beams below. Using singularity functions, calculate the deflection at 2 metres, the deflection at the tip, and sketch the deflected shape. The cross section of the beam is 300 mm deep by 200 mm wide, and it is made of concrete with a Young’s modulus of 30,000 MPa.

4. Using singularity functions, derive (in terms of P) the equation for the upwards deflection at midspan of the beam below. EI = 10 x 106 Nm2

5. Determine the location and value of the maximum deflection for the beam below. How far from the centre is the point of maximum deflection (expressed as a percentage of the span length)? EI = 10 x 106 Nm2

6. Calculate the reactions and draw the shear force and bending moment diagrams for the beam below. EI = 10 x 106 Nm2
(Note that this has four reactions, so the 3 equations of equilibrium do not give sufficient information to solve the problem – it is statically indeterminate. The answer requires you to use the results from questions 4 and 5).

7. For the beam below, use singularity functions to determine an equation for the deflected shape, expressed in terms of x (measured from the left) and EI. If the beam is made of timber (E = 10,000 MPa) and the cross section is 200 mm x 50 mm, what is the maximum downward deflection (in mm), and is the beam stiff enough if the maximum deflection should not exceed span/250 (the span is always measured between two adjacent supports).

8. Determine the location and value of the maximum deflection for the beam below. How far from the…...

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