Problem 3 - Figure 4 shows a symmetrical one-story structure. Each column has an individual stiffness of k = 5.Okip/in. Each way. The roof girders have an infinite stiffness relative to the columns. Required A. Develop a lumped mass mathematical model of the structure that will be suitable for use in the analysis for the spectrum shown. Assume 2% damping ratio. B. Using El-Centro response spectrum, determine the maximum earthquake force in the X-X direction applied to the roof level. C. Determine the maximum column share for the force in Part B. D. Determine the maximum deflection of the roof in the X-X direction 12' 20' X 20' Fig. 3 Total roof weight = 40 lb/ft^2 Rigid girders (typical) Column stiffness k =5.0 k/in. each way Weight walls = 15 lb/ft^2 all sides of building RESPONSE SPECTRUM IMPERIAL VALLEY EARTHQUAKE MAY 18, 1940 - 2037 PST IIIA001 40.001.0 EL CENTRO SITE IMPERIAL VALLEY IRRIGATION DISTRICT COMP SOOE DAMPING VALUES ARE O. 2. 5. 10 AND 20 PERCENT OF CRITICAL 400 200 F80 Acceleration, g 80 60 40 8884 100 20 20 086 4 VELOCITY (in./sec) .8 201 02 800 006 004 002 الله 2 86 Displacement, in. -20 400 008- 600 400 200 60 200 100 80 60 -800 40 20 20 006 004+ 10 986 F2000 4 2 0013 8000 0006 0004 .8 .6 2 4 6810 PERIOD (secs) .1 .04 .06.08.1 .2 4 .6.81 20 4 2 20 20

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

Two line loads q1 and q2 of infinite lengths are acting on top of an elastic medium, as shown in Figure P8.6. Find the vertical stress increase at A.

Refer to Figure 10.43. A strip load of q = 1450 lb/ft2 is applied over a width with B = 48 ft. Determine the increase in vertical stress at point A located z = 21 ft below the surface. Given x = 28.8 ft. Figure 10.43