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Chapter 8.5, Problem BYGV
To determine

Explain the meaning for the terms “Instantaneous Acceleration”, “Angular Speed”, and “Volume Flow Rate”.

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As shown in the figure below, a 1.5 m × 1.5 m footing is carrying a 400 kN load. P Depth (m) 0.0 1.0 2.0 Df Groundwater table (Yw = 9.81 kN/m³) 3.5 Yt = 16.5 kN/m³ E = 9,000 kPa Sandy soil Ysat 17.5 kN/m³ E = 15,000 kPa 6.0 Stiff Clay (OCR = 2) Bedrock Ysat 18.0 kN/m³ eo = 0.8 Cc = 0.15, Cr = 0.02 Eu =40,000 kPa (a) Estimate the immediate settlement beneath the center of the footing. Assuming that Poisson's ratios of sand and soft clay are 0.3 and 0.5, respectively. Use numerical integration approach. For the calculations, use layers (below the bottom of the footing) of thicknesses: 1 m; 1.5 m, and 2.5 m. (b) Determine the primary consolidation settlement beneath the center of the footing. (c) Redo Part (b) if OCR=1.1. Note: Use the 2:1 method to determine the stress increase below the footing. For parts (b) and (c), use the one-dimensional consolidation theory.
Consider the cross-sections illustrated in the next slides. Implement a cross-sectional analysis based on a layered discretisation of the cross- section as required at the following. 1) Develop the implementation of an analysis to estimate the nonlinear response of the composite steel-concrete section, of the reinforced concrete section and of the steel section shown in following slides (using material nonlinear models provided in the support files). Provide the details of the numerical implementation with clear explanations of all steps. Hint: the implementation can be done in Excel. 2) Discuss how the 3 cross-sections (shown in the next slides) compare to each other in terms of embodied carbon under the condition that the cross-sections possess the same nominal moment capacity (i.e. the peak moment achieved in the moment-curvature diagram). The discussion should include at least 2 sets of the sections (each set contains one composite section, one reinforced concrete section and one…
Consider the following static route choice problem where 110 vehicles travel from point A to point B. The corresponding travel time (in minutes) of each link is as follows: t₁ = x1; t₂ = x2 + 20; t3x3 + 10; t₁ = 3×4 where Xi denotes the number of vehicles that choose link i. Find the number of vehicles that travel on each link when a. The user equilibrium condition (UE) is satisfied, where vehicles select the route with the minimum travel time; and b. The system optimum condition (SO) is satisfied, where the total travel time is minimised. C. Report the total delay savings when satisfying SO instead of UE. 2 B A 3 4
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