Note:
REVIEW INNOVATIONS
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Situation 1. The section of a column column is shown in the figure. figure. For this problem, b1 = 300 mm, b2 = 180 mm, d1 = 250 mm, d2 = 350 mm, f’ mm, f’c = 28 MPa, f MPa, f y = 414 MPa. �
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Part (2): Plastic centroid Plastic centroid is the location of the resultant force produced by the steel and concrete. F concrete concrete = 0.85 f’c Ac � ������ ����� F steel = f y As steel = f
Another Solution by Engr. Romel Tarcelo F. Verterra Author, MATHalino.com
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Part (3): e = 400 − 290 = 110 mm = 0.11 m M u = Pu e = 3200(0.11) = 352 kN m ⋅
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Determine the location of the centroid of the gross concrete area measured from y-axis. A. 281 B. 262 C. 274 D. 253 Determine the location of of the plastic neutral neutral axis of of the column measured from the y-axis, in mm. Neglect the area of concrete occupied by the steel. A. 272 B. 302 C. 282 D. 292 Determine the factored moment M moment M u, in kN⋅m, due to a factored load Pu = 3200 kN applied 400 mm from the yaxis. Assume that the column is reinforced such that plastic neutral axis is 290 mm from the y-axis. A. 352 B. 387 C. 326 D. 376
Situation 2. For the section shown below, determine determine the following: 4. The value of y . A. 200 mm B. 206 mm C. 208 mm D. 202 mm 5. Moment of inertia inertia with respect respect to the centroidal x-axis. A. 240 × 106 mm4 C. 50.8 × 106 mm4 6 4 B. 260 × 10 mm D. 80.5 × 106 mm4 6. Moment of Inertia with respect to the centroidal y-axis. A. 240 × 106 mm4 C. 50.8 × 106 mm4 B. 260 × 106 mm4 D. 80.5 × 106 mm4 ��� ��
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Solution
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REVIEW INNOVATIONS
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Situation 4. Given the sequence 2, 6, 18, 18, 54, … 12. Find the 12th term 13. Find n if an = 9,565,938. 14. Find the sum of the first ten terms.
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150(20 150(203 ) 20(300 20(3003 ) 300(20 300(203 ) I NA = + + + Σ� NA 12 12 12 4 I NA NA = 260 340 000 mm
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Part (3)
Part : 12th term = 1ŷ = 354 294 Part : n = �������� = 15 Part : S = Σ(�ŷ,1,10) = 59 048
20(150 20(1503 ) 300(20 300(203 ) 20(300 20(3003 ) I y = + + 12 12 12 I y = 50 825 000 mm4
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Situation 3. The 3 term of an arithmetic progression is 11 and the 10th term is 32. 7. Find the 16th term. A. 50 B. 53 C. 44 D. 47 8. What is the common difference? A. 4 B. 2 C. 5 D. 3 th 9. If the n term is 83, what is n? A. 35 B. 27 C. 25 D. 37 10. Calculate the sum of the first 50 terms. A. 3925 B. 2924 C. 1025 D. 5610 11. What is n so that the sum of the first n terms is 874? A. 30 B. 27 C. 25 D. 23
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15. A man invested invested P10,000.00 per month on a bank that offers interest of 6% compounded compounded monthly. How much can he get after 5 years? A. P600,000.00 C. P725,400.00 B. P697,700.00 D. P700,000.00 Solution i = 6%÷12 = 0.5% = 0.005 n = 12(5) = 60 ���� 3����� 3����� ��� ⋅���
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Part : 16th term = 1�ŷ = 50 Part : Common difference = 2ŷ � 1ŷ = 3 Part : n = ��� = 27 Part : S = Σ(�ŷ,1,50) = 3925 use the choices Part : S = Σ(�ŷ,1,23) = 874 ˆ
16. A sphere of diameter diameter 40 c m is cut by two horizontal planes. One plane is 8 cm cm below the center center of the sphere and the other is 14 cm above the center of the sphere. Determine the volume of the frustum frustum formed between the cutting planes. ��� ��
Solution
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Another way to solve for Part : This approach is very convenient if the first three terms are given. For this problem, the the first three terms are a1 = 5, a2 = 8, and a3 = 11 3�����
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F = = Σ(�ŷ,1,�0)= P697,700.30
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Solution
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( BX + CX 2 )dX = 24 236.34 cm3
