reinforaced concrete A reinforced concrete beam continuous over four spons and i

Question

reinforaced concrete A reinforced concrete beam continuous over four spons and integral with columns at the ends is shown. The clear distance between supports is 105 feet and the beam supports a factored load of 10 kips/ ft. Design Assumptions: ACI code. You must shown your work and your selection on your paper and not here. (a) The design shear force at the face of the first interior support is most nearly A 75 kips B 79 kips c. 82 kips D. 86 kips (b) The design shear force at the face of the outer support is most nearly A 75 kips B 79 kips C. 82 kips D. 86 kips (c) The design moment at the outer support t most nearly A 40 kips B 160 kips C 205 ft- kips d. 230 ft. kips (d) The design moment at the first interior support Is most nearly A. 140 ft-kips 8. 160 ft- kips C. 205 ft- kips D. 230 ft.kips (e) The design moment at the center support Is most nearly A 140 ft- kips B. 160 ft- kips C. 205 ft.kips D. 230 ft- kips (f) The design moment in the first span a most nearly A. 140 ft-kips B. 160 ft-kips C. 205 ft.kips D. 230 ft- kips (g) The design moment in the second span is most neatly A. 40 ft-kips B. 160 ft-kips C. 205 ft-kips D. 230 ft-kips

Explanation / Answer

Solution:

As per ACI Code ,

Shear force at outer span = (1.15 x uniformly distributed load x span length ) / 2

Shear force at interior span = ( uniformly distributed load x span length ) / 2

In the given problem,

At first interior support = ( 10 x 15 ) / 2 = 75 Kips, so that answer for (a) is A

Shearforce at outer span = ( 1.15 x 10 x 15 ) / 2 = 86.25 Kips, so that answer for (b) is D

In bending moment diagram:

support of continuous beam feels possitive moment ,

span of continuous beam feels negative moment.

As per ACI standard,

(c) At outer support M = ( W x l2 ) / 16,

Here, M = ( 10 x 152 ) / 16 = 140.625 Kips. , so that , answer for (c) is A.

(d) At first interior support M = ( W x l2 ) / 11,

Here, M = ( 10 x 152 ) / 11 = 204.5454 Kips. , so that , answer for (d) is C.

(e) At center support M = ( W x l2 ) / 10,

Here, M = ( 10 x 152 ) / 10 = 225 Kips. , so that , answer for (e) is D.

(f) At End span M = ( W x l2 ) / 14,

Here, M = ( 10 x 152 ) / 14 = 160.71 Kips. , so that , answer for (f) is B.

(g) At Second span M = ( W x l2 ) / 16,

Here, M = ( 10 x 152 ) / 14 = 140.625 Kips. , so that , answer for (g) is A.

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