Solution Manual Vol 7

9 at failure a 023 chapter 5 stresses and

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Unformatted text preview: tained from Figure 5.10. In this case z 4 250 Ir kN=m2 1 mn z 30 Stresses and displacements z (m) 0 0.5 1 1.5 2 3 4 7 10 m, n 2.00 1.00 0.67 0.50 0.33 0.25 0.14 0.10 Ir 0.233 0.176 0.122 0.085 0.045 0.027 0.009 0.005 z (kN/m2) (250) 233 176 122 85 45 27 9 5 z is plotted against z in Figure Q5.3. Figure Q5.3 5.4 (a) m 12:5 1:04 12 18 n 1:50 12 From Figure 5.10, Ir 0.196. ; z 2 175 0:196 68 kN=m2 Stresses and displacements 31 Figure Q5.4 (b) The foundation is drawn on Newmark's chart as shown in Figure Q5.4, the scale line representing 12 m (z). Number of influence areas (N ) 78. ; z 0:005 Nq 0:005 78 175 68 kN=m2 5.5 Q 150 kN/m; h 4.00 m; m 0.5. The total thrust is given by Equation 5.18 Px 2Q 1 2 150 76 kN=m m2 1 1:25 Equation 5.17 is used to obtain the pressure distribution px 4Q m2 n 150 m2 n kN=m2 2 h m2 n2 m2 n2 2 32 Stresses and displacements n 0 0.1 0.2 0.3 0.4 0.6 0.8 1.0 (m2 m2 n n2 )2 px (kN/m2 ) 0 17.7 28.4 31.0 28.4 19.2 12.0 7.6 0 0.370 0.595 0.649 0.595 0.403 0.252 0.160 The pressure distribution is plotted in Figure Q5.5. Figure Q5.5 5.6 H 10 5 B 2 L 4 2 B 2 D 1 0:5 B 2 Hence from Figure 5.15 1 0:82 0 0:94 Stresses and displacements 33 The immediate settlement is given by Equation 5.28 si 0 1 qB Eu 200 2 7 mm 45 0:94 0:82 Chapter 6 Lateral earth pressure 6.1 For 0 37 the active pressure coefficient is given by Ka 1 sin 37 0:25 1 sin 37 The total active thrust (Equation 6.6a with c0 0) is 1 1 Pa Ka H 2 0:25 17 62 76:5 kN=m 2 2 If the wall is prevented from yielding, the at-rest condition applies. The approximate value of the coefficient of earth pressure at-rest is given by Equation 6.15a K0 1 sin 0 1 sin 37 0:40 and the thrust on the wall is 1 1 P0 K0 H 2 0:40 17 62 122 kN=m 2 2 6.2 The active pressure coefficients for the three soil types are as follows: Ka1 Ka2 Ka3 1 sin 35 0:271 1 sin 35 1 sin 27 0:375; 1 sin 27 1 sin 42 0:198 1 sin 42 pffiffiffiffiffiffiffi Ka2 0:613 Lateral earth pressure 35 Distribution of active pressure (plotted in Figure Q6.2): Depth (m) Soil Active pressure (kN/m2) 3 5 5 8 8 12 1 1 2 2 3 3 0:271 16 3 13:0 (0:271 16 3) (0:271 9:2 2) 13:0 5:0 18:0 f(16 3) (9:2 2)g 0:375 (2 17 0:613) 24:9 20:9 4:0 4:0 (0:375 10:2 3) 4:0 11:5 15:5 f(16 3) (9:2 2) (10:2 3)g 0:198 19:2 19:2 (0:198 11:2 4) 19:2 8:9 28:1 At a depth of 12 m, the hydrostatic pressure 9:8 9 88:2 kN/m2 . Calculation of total thrust and its point of application (forces are numbered as in Figure Q6.2 and moments are taken about the top of the wall) per m: Total thrust 571 kN/m. Point of application is (4893/571) m from the top of the wall, i.e. 8.57 m. Force (kN) (1) (2) (3) (4) (5) (6) (7) (8) 1 0:271 16 32 19.5 2 0:271 16 3 2 26.0 1 2 0:271 9:2 2 5.0 2 [0:375 f(16 3) (9:2 2)g f2 17 0:613g] 3 12.2 1 0:375 10:2 32 17.2 2 [0:198 f(16 3) (9:2 2) (10:2 3)g] 4 76.8 1 2 17.7 0:198 11:2 4 2 1 9:8 92 396.9 2 571.3 Arm (m) 2.0 4.0 4.33 6.5 7.0 10.0 10.67 9.0 Moment (kN m) 39.0 104.0 21.7 79.3 120.4 768.0 188.9 3572.1 4893.4 Figure Q6.2 36 Lateral earth pressure 6.3 (a) For u 0, Ka Kp 1 pffiffiffiffiffiffiffi Kac Kpc 2 1:5 2:45 At the lower end of the piling: pa Ka q Ka sat z Kac cu 1 18 3 1 20 4 2:45 50 54 80 122:5 11:5 kN=m2 pp Kp sat z Kpc cu 1 20 4 2:45 50 80 122:5 202 kN=m2 1 (b) For 0 26 and 0 2 Ka 0:35 pffiffiffiffiffiffiffiffiffiffiffi...
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This note was uploaded on 09/21/2009 for the course CVEN 3718 taught by Professor Dobroslavznidarcic during the Spring '08 term at Colorado.

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