Problem 4 In Figure 4, a 5-kg uniform serving table is supported on each side by two pairs of identical links, AB and CD, and springs CE. If the bowl has a mass of 1 kg and is in equilibrium when = 45°, and the springs of stiffness k each are unstretched when 0 = 90°. Neglect the mass of the links. (a) Draw the free body diagram. You need to specify the positions of the gravity center of the bowl (yGb) and table (yot) as well as the deformation of the spring (xc) (b) Express yGb, yGt and xc in terms of 0. (c) Find the virtual displacements SyGь, SyGt and Sxc of the positions due to a virtual rotation Se. (d) Write the virtual work equation. 250 mm 150 mm (e) Determine the stiffness of each spring. 250 mm Figure 4 k 150 mm

A beam is part of the framing system for the floor of an office building. The floor is subjected to both dead loads and live loads. The maximum moment caused by the service dead load is 45 ft-kips, and the maximum moment for the service live load is 63 ft-kips (these moments occur at the same location on the beam and can therefore be combined). a. If load and resistance factor design is used, determine the maximum factored bending moment (required moment strength). What is the controlling AISC load combination? b. What is the required nominal moment strength for a resistance factor of 0.90? c. If allowable strength design is used, determine the required moment strength. What is the controlling AISC lead combination? d. What is the required nominal moment strength for a safety factor of 1.67?

EB and FG are two planes inside a soil element ABCD as shown in Figure 10.50. Stress conditions on the two planes are Plane EB: EB = 25 kN/m2; EB = +10 kN/m2 Plane FG: FG = 10 kN/m2; FG = 5 kN/m2 (Note: Mohrs circle sign conventions for stresses are used above) Given ; = 25, determine: a. The maximum and minimum principal stresses b. The angle between the planes EB and FG c. The external stresses on planes AB and BC that would cause the above internal stresses on planes EB and FG

A 9 ft wide and infinitely long flexible strip load of 800 lb/ft2 is placed on an elastic medium as shown in Figure P8.7. Find the vertical stress increase at points A, B, and C located 3 ft below the surface.

The soil profile at a site is shown Figure P16.3. Find the total horizontal normal stresses at A and B, assuming at-rest conditions.

Compare the engineering and true secant elastic moduli for the natural rubber in Example Problem 6.2 at an engineering strain of 6.0. Assume that the deformation is all elastic.

A column in a building is subjected to the following load effects: 9 kips compression from dead load 5 kips compression from roof live load 6 kips compression from snow 7 kips compression from 3 inches of rain accumulated on the roof 8 kips compression from wind a. If lead and resistance factor design is used, determine the factored load (required strength) to be used in the design of the column. Which AISC load combination controls? b. What is the required design strength of the Column? c. What is the required nominal strength of the column for a resistance factor of 0.90? d. If allowable strength design is used, determine the required load capacity (required strength) to be used in the design of the column. Which AISC load combination controls? e. What is the required nominal strength of the column for a safety factor of 1.67?