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**Resistência dos Materiais, 5ª ed.**

13 – Flambagem de Colunas R.C. Hibbeler ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_00CO.TIF Notes:**

The columns for this building are used to support the floor loading. Engineers design ©2004 by Pearson Education

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FG13_01a.TIF Notes: critical load ©2004 by Pearson Education

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FG13_01b.TIF Notes: critical load ©2004 by Pearson Education

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FG13_02a.TIF Notes: critical load ©2004 by Pearson Education

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FG13_02b.TIF Notes: critical load ©2004 by Pearson Education

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FG13_02c.TIF Notes: critical load ©2004 by Pearson Education

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FG13_03.TIF Notes: stages of equlibrium ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_03-01UN.TIF Notes:**

Some pin-connected members used in moving machinery ©2004 by Pearson Education

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FG13_04a.TIF Notes: ideal column ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_04b.TIF Notes:**

column with small lateral force, F ©2004 by Pearson Education

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FG13_04c.TIF Notes: column with F removed ©2004 by Pearson Education

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FG13_05a.TIF Notes: n=1 ©2004 by Pearson Education

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FG13_05a_repeat.TIF Notes: n=1 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_05b.TIF Notes:**

ideal column with pin supports ©2004 by Pearson Education

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FG13_05c.TIF Notes: curvy column, n = 2 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_06.TIF Notes:**

column with bifurcation point ©2004 by Pearson Education

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FG13_07.TIF Notes: meter stick ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_07-01UN.TIF Notes:**

typical interior steel pipe columns used to support the roof of a single story bldg ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_08.TIF Notes:**

structural steel, aluminum alloy graph curves ©2004 by Pearson Education

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FG13_09.TIF Notes: Example 13-1 ©2004 by Pearson Education

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FG13_10.TIF Notes: Example 13-2 ©2004 by Pearson Education

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FG13_11a.TIF Notes: buckling of columns ©2004 by Pearson Education

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FG13_11b.TIF Notes: buckling of columns ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_11-01UN.TIF Notes:**

tubular columns used to support this water tank have been braced at 3 locations ©2004 by Pearson Education

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FG13_12a.TIF Notes: pinned ends ©2004 by Pearson Education

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FG13_12b.TIF Notes: fixed and free ends ©2004 by Pearson Education

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FG13_12c.TIF Notes: fixed ends ©2004 by Pearson Education

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FG13_12d.TIF Notes: pinned and fixed ends ©2004 by Pearson Education

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FG13_13a.TIF Notes: Example 13-3 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_13b.TIF Notes:**

Example 13-3 (x-x axis buckling) ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_13c.TIF Notes:**

Example 13-3 (y-y axis buckling) ©2004 by Pearson Education

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FG13_14a.TIF Notes: Example 13-4 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_14b.TIF Notes:**

Example 13-4 (x-x axis buckling) ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_14c.TIF Notes:**

Example 13-4 (y-y axis buckling) ©2004 by Pearson Education

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FG13_14-01UNP01.TIF Notes: Problem 13-1 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_14-02UNP02_03.TIF Notes:**

Problem 13-2/13-3 ©2004 by Pearson Education

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FG13_14-03UNP04.TIF Notes: Problem 13-4 ©2004 by Pearson Education

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FG13_ UNP05.TIF Notes: Problem 13-5 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_14-04UNP06_07.TIF Notes:**

Problem 13-6/7 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_14-05UNP08_09.TIF Notes:**

Problem 13-8/9 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_14-06UNP10_11.TIF Notes:**

Problem 13-10/11 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_14-07UNP12_13.TIF Notes:**

Problem 13-12/13-13 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_14-08UNP14_15.TIF Notes:**

Problem 13-14/13-15 ©2004 by Pearson Education

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FG13_14-09UNP16.TIF Notes: Problem 13-16 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_14-10UNP17_18.TIF Notes:**

Problem 13-16/17 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_14-11UNP19_20.TIF Notes:**

Problem 13-19/13-20 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_14-12UNP21_22.TIF Notes:**

Problem 13-21/22 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_14-13UNP23_24.TIF Notes:**

Problem 13-23/24 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_14-14UNP25_26.TIF Notes:**

Problem 13-25/26 ©2004 by Pearson Education

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FG13_14-15UNP27.TIF Notes: Problem 13-27 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_14-16UNP28.TIF Notes:**

Problem (repeat of Problem 13-27) ©2004 by Pearson Education

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FG13_14-17UNP29.TIF Notes: Problem 13-29 ©2004 by Pearson Education

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FG13_14-18UNP30.TIF Notes: Problem 13-30 ©2004 by Pearson Education

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FG13_14-19UNP31.TIF Notes: Problem 13-31 ©2004 by Pearson Education

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FG13_14-20UNP32.TIF Notes: Problem 13-32 ©2004 by Pearson Education

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FG13_14-21UNP33.TIF Notes: Problem 13-33 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_14-22UNP34_35.TIF Notes:**

Problem 13-34/35 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_14-23UNP36_37.TIF Notes:**

Problem 13-36/13-37 ©2004 by Pearson Education

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FG13_14-24UNP38.TIF Notes: Problem 13-38 ©2004 by Pearson Education

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FG13_14-25UNP39.TIF Notes: Problem 13-39 ©2004 by Pearson Education

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FG13_14-26UNP40.TIF Notes: Problem 13-40 ©2004 by Pearson Education

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FG13_14-27UNP41.TIF Notes: Problem 13-41 ©2004 by Pearson Education

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FG13_14-28UNP44.TIF Notes: Problem 13-44 ©2004 by Pearson Education

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FG13_14-29UNP45.TIF Notes: Problem 13-45 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_14-30UN.TIF Notes:**

these timber columns can be considered pinned at their bottom ©2004 by Pearson Education

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FG13_15a.TIF Notes: the secant formula ©2004 by Pearson Education

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FG13_15b.TIF Notes: the secant formula ©2004 by Pearson Education

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FG13_15c.TIF Notes: the secant formula ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_16.TIF Notes:**

ideal column (small deflections), inelastic behavior ©2004 by Pearson Education

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FG13_17a.TIF Notes: column diagrams ©2004 by Pearson Education

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FG13_17b.TIF Notes: varoius types of stress ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_18.TIF Notes:**

Euler's formula, A-36 structural steel ©2004 by Pearson Education

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FG13_19.TIF Notes: Example 13-5 ©2004 by Pearson Education

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FG13_20a.TIF Notes: Example 13-6 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_20b.TIF Notes:**

Example 13-6 (y-y axis buckling) ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_20c.TIF Notes:**

Example 13-6 (x-x axis buckling) ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_20-01UN.TIF Notes:**

crane boom failed by buckling caused by an overload ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_20-02UN.TIF Notes:**

crane boom failure; localized collapse ©2004 by Pearson Education

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FG13_21a.TIF Notes: slope at point D ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_21b.TIF Notes:**

inelastic and elastic columns ©2004 by Pearson Education

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FG13_22.TIF Notes: Example 13-7 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_22-01UNP46_47.TIF Notes:**

Problem 13-46/47 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_22-02UNP48_49.TIF Notes:**

Problem 13-48/49 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_22-03UNP50_52.TIF Notes:**

Problem 13-50/51/52 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_22-04UNP53_54.TIF Notes:**

Problem 13-53/54 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_22-05UNP55_56.TIF Notes:**

Problem 13-55/56 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_22-06UNP57_58.TIF Notes:**

Problem 13-57/58 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_22-07UNP59_60.TIF Notes:**

Problem 13-59/60 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_22-08UNP61_62.TIF Notes:**

Problem 13-61/62 ©2004 by Pearson Education

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FG13_22-09UNP63.TIF Notes: Problem 13-63 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_22-10UNP64_65.TIF Notes:**

Problem 13-64/65 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_22-11UNP67_69.TIF Notes:**

Problem 13-67/68/69 ©2004 by Pearson Education

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FG13_22-12UNP70.TIF Notes: Problem 13-70 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_22-13UN.TIF Notes:**

these long unbraced timber columns are used to support the roof of this building ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_23.TIF Notes:**

Euler formula for short, intermediate and long columns ©2004 by Pearson Education

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FG13_24.TIF Notes: Eq and Eq 13-21 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_25.TIF Notes:**

Eq 13-24, and 13-26 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_26.TIF Notes:**

Eq 13-27, and 13-29 ©2004 by Pearson Education

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FG13_27.TIF Notes: Example 13-8 ©2004 by Pearson Education

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FG13_28.TIF Notes: Example 13-9 ©2004 by Pearson Education

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FG13_29.TIF Notes: Example 13-10 ©2004 by Pearson Education

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FG13_30.TIF Notes: Example 13-11 ©2004 by Pearson Education

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FG13_30-01UNP79.TIF Notes: Problem 13-79 ©2004 by Pearson Education

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FG13_30-02UNP84.TIF Notes: Problem 13-84 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_30-03UNP85_86.TIF Notes:**

Problem 13-85/86 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_30-04UNP87_88.TIF Notes:**

Problem 13-87/88 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_30-05UNP91_93.TIF Notes:**

Problem 13-91/92/93 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_30-06UNP95_96.TIF Notes:**

Problem 13-95/96 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_30-07UNP97_98.TIF Notes:**

Problem 13-97/98 ©2004 by Pearson Education

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FG13_30-08UNP99.TIF Notes: Problem 99 ©2004 by Pearson Education

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FG13_30-09UNP100.TIF Notes: Problem 100 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_31a.TIF Notes:**

design of columns for eccentric loading ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_31b.TIF Notes:**

ideal column with pin supports ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_31-01UN.TIF Notes:**

typical example of a column used to support an eccentric roof loading ©2004 by Pearson Education

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FG13_32.TIF Notes: Example 13-12 ©2004 by Pearson Education

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FG13_33.TIF Notes: Example 13-13 ©2004 by Pearson Education

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FG13_34.TIF Notes: Example 13-14 ©2004 by Pearson Education

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FG13_34-01UNP101.TIF Notes: Problem ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_34-02UNP102.TIF Notes:**

Problem (repeat of Problem ) ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_34-03UNP103_106.TIF Notes:**

Problem /104/ 105/106 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_34-04UNP107_109.TIF Notes:**

Problem /108/109 ©2004 by Pearson Education

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FG13_34-05UNP110.TIF Notes: Problem ©2004 by Pearson Education

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FG13_34-06UNP111.TIF Notes: Problem ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_34-07UNP112_113.TIF Notes:**

Problem /113 ©2004 by Pearson Education

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FG13_34-08UNP114.TIF Notes: Problem ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_34-09UNP115.TIF Notes:**

Problem (repeat of Problem ) ©2004 by Pearson Education

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FG13_34-10UNP116.TIF Notes: Problem ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_34-11UNP117.TIF Notes:**

Problem (repeat of Problem ) ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_34-13UNP119_120.TIF Notes:**

Problem /120 ©2004 by Pearson Education

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FG13_34-14UNP121.TIF Notes: Problem ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_34-15UNP122.TIF Notes:**

Problem (repeat of Problem ) ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_34-16UNP123_124.TIF Notes:**

Problem /124 ©2004 by Pearson Education

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**©2004 by Pearson Education FG13_34-17UNP125_126.TIF Notes:**

Problem /126 ©2004 by Pearson Education

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FG13_34-19UNP128.TIF Notes: Problem 128 ©2004 by Pearson Education

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