A 200-lb block is at rest on a 30° inclined plane. The coefficient of friction between the block and the inclined plane is 0.20. Compute the value of a horizontal force P that will cause motion to impend the block up the inclined plane. 200 lb P 30°

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Problem 1 = = = 13,600 Manometers can be used in combination with cardiovascular catheters to measure blood pressure based on height differences. In the example in Figure 1, the manometer contains two fluids: water (density p 995 Kg/m³) and mercury (density pm Kg/m³). The density of blood is p 1,060 Kg/m³. Assume that there is atmospheric pressure at the interface between mercury and air. The interface between mercury and water is at z₁ = 7 cm, the interface between water and blood is at Z2 27 cm, and the tip of the manometer at za 10 cm. Recall that the fluid statics equation is dp/dz-pg 0, when the z axis is taken pointing downwards. a. What is the gauge pressure po at the interface with air, in mmHg? (5 points) b. Calculate the gauge pressure ps at the tip of the manometer, in mmHg. (5 points) N Z37 blood ப Zz Water Mercury Zo 3=0 z Figure 1. Manometer for blood pressure measurement.

Determine the following for the beam with unknown loading, using the Shear and Bending Diagrams provided in the figures on the right: a. The maximum shear stress experienced by the beam. b. The maximum flexural stress experienced by the beam (Indicate if this is tensile or compressive flexural stress) c. The loading diagram (Indicate the magnitudes of the loading/s. The loads are acting along the plane of symmetry of the section) 20 80 20 十十 SHEAR DIAGRAM x=577.3502692 mm 20 KN 1° 5/3 KN 2° C 2° D A B CROSS SECTION Dimensions are in mm LOADING DIAGRAM ? 120 40 40 A B C D 1000mm 2000mm 1000mm -55/3 KN MB' C D BENDING DIAGRAM MB A B Σ Mc

Find the maximum bending stress in ksi for this beam if it is made from a W16x50 steel shape. If the steel yields at 50 ksi, will the beam support the loads shown without permanently deforming? Confirm the max moment in the beam by drawing the shear and moment diagram. 18 kip-ft 2 kip/ft 9 ft

Problem 4 A propped cantilever beam of flexural rigidity EI and 2EI for parts 1-2 and 2-3, respectively, is subjected to a concentrated load P at point 2. Find: a) Determine the displacement at point 2; b) Determine the rotation at point 3; c) Determine the reaction force and moment at point 1; d) Determine the reaction force at point 3. El 2 P 2 EI 2 L

Problem 3 15 A W150 x 37 rolled-steel beam is used below. Let P150 kN, L-10 m and E 200 GPa. Find the deflection and slope at each node and each pin or wall reaction. If a software program such Maple or MATLAB issued as part of the solution, a hard copy of the code must be submitted too. 1/2 1/2

1. Determine the bearings, azimuths, and lengths of lines AB, BC, CD, and DA for the closed loop traverse data shown below in Table 1. Show calculations. Table 1 Station Northing [ft] Easting [ft] A 1,000 1,000 B 750 1,750 C 1,345 2,255 D 1,567 1,345 2. Compute the bearings of sides BC and CD in Figure 1. Show all work for all angles. A B 70°10' S72°39'W C 94°35' Figure 1 Tt (+) B D

hoph - AT 10x AT 10.076 ht 0.076 0 0-1846112 14884 xh T 1.632m h-4- (1-22) h = 1.022m 14. The 4-ft-diameter cylinder, 4 ft long, is acted upon by water on the left and oil of sp gr 0.800 on the right. Determine (a) the normal force at B if the cylinder weighs 4000 lb and (b) the horizontal force due to oil and water if the oil level drops 1 ft. Solution Water Oil B