Title MSTE 37 Solutions.pdf ✅

B = 10 m ▣ 4. From the following cross-section notes for a road grading work, the road is bed 9 m wide and the side slope is 1:1 for cut and 1.5:1 for fill. Determine the area of the cut section. -3.2 +1.2 +1.2 +2.8 x1 0 3.5 x2 [SOLUTION] a + 4.8 3.2 = 4.5 − a 1.2 a = 108 55 m Acut = 1 2 (4.5 − a)(1.2) + (1.2)(3.5) + 1 2 (1.2)(3.8) + 1 2 (1.0)(2.8) Acut = 9.4018 m2 SITUATION 1. The following data area cross-section notes of the ground which will be excavated for a roadway. The base is 10 m and the side slopes are 1.5:1. Sta 4+120 Sta 4+160 8 0 9.2 9.5 0 10.7 +2 +3.2 +2.8 +3 +2.6 +3.8 [PRE-SOLUTION] At Sta 4+120
A1 = 1 2 (5)(2) + 1 2 (3.2)(8) + 1 2 (3.2)(9.2) + 1 2 (5)(2.8) A1 = 39.52 m2 At Sta 4+160 A2 = 1 2 (5)(3) + 1 2 (2.6)(9.5) + 1 2 (2.6)(10.7) + 1 2 (5)(3.8) A2 = 43.26 m2 ▣ 5. Determine the volume by end area method. [SOLUTION] Ve = L 2 (A1 + A2 ) Ve = 40 2 (39.52 + 43.26) Ve = 1655.60 m3 ▣ 6. In the previous question, determine the volume by prismoidal formula. [SOLUTION] c1 = 8 + 9.2 = 17.2 c2 = 9.5 + 10.7 = 20.2 Vcp = L 12 (d2 − d1 )(c2 − c1 ) Vcp = 40 12 (2.6 − 3.2)(20.2 − 17.2) = −6 m3 Vp = 1655.60 − (−6) = 1661.60 m3