Derive the following relations for the the limit state design of balanced rectangular RCC beam (a) Depth of the neutral axis, X, = 0.479 d (b) Limiting BM, M, = 0.138 f bd2 (c) Steel area, A = 4.78 x 10-4 f bd Where, %3D ck Width of beam = b Depth of beam = d Characteristic strength of concrete = f, MPa ck Characteristic strength of steel = 415 MPa and modulus of elasticity of steel = 2 x 105 MPa

Derive the following relations for the the limit state design of balanced rectangular RCC beam (a) Depth of the neutral axis, X, = 0.479 d (b) Limiting BM, M, = 0.138 f bd2 (c) Steel area, A = 4.78 x 10-4 f bd Where, %3D ck Width of beam = b Depth of beam = d Characteristic strength of concrete = f, MPa ck Characteristic strength of steel = 415 MPa and modulus of elasticity of steel = 2 x 105 MPa

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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70 mm 500 mm 640 mm 70 mm 70 mm -70 mm 210 mm -350 mm- The column section shown above is reinforced with equal number of 20 mm bars on each face. Using f.-21 MPa, long bar f, = 420 MPa, calculate the following: 1. The distance of the neutral axis "e" (mm) from the extreme concrete compression fiber at balanced condition with bending about x-axis. с 335 The compressive force on concrete compression area (kN) when section fails A. 285 В. 320 D. 275 2. at balanced condition with bending about the x-axis. A. 1,780 kN B. 3,255 kN C. 2,094 kN D. 1,690 kN 3. The internal force in the 2 bars at the middle when the section fails at balanced condition with bending about the x-axis. C. 10.81 kN A. 11.71 kN B. 17.19 kN D. 28.34 kN
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A rectangular beam has a width of 285 mm and an effective depth of 520mm. It is reinforced with 4 – 36 mm ø bars having fy = 430 MPa. If he compressivestrength of the concrete is 28MPa, find the following a. Location of the neutral axis from the top of the beam.b. Stress of the steel.c. Ultimate capacity of the beam?
Given the properties of a reinforced concrete beam with section below: Unit weight of concrete = 24 kN/m3 %3D • Concrete compressive strength = %3D 34.5 MPa Steel yield strength = 420 MPa %3D b = 250 mm ; width of the beam h = 500 mm ; depth of the beam %3D %3D Steel area = 4-28 mm o Diameter of stirrups 12 mm %3D Calculate the following: 1. Reduction factor o 2. Moment Capacity (nominal) of the beam in kN-m 3. Assuming the beam to be simply supported with 7 m span, determine the maximum concentrated dead load that it can carry at midspan along with it's self-weight in kN
A beam having a width of 500 mm and a total depth of 800mm is reinforced with 6-32mm dia bars, Compressive strength of concrete is 28 MPa and yield strength of reinforcing bars is 420MP.. 640 mm 800 mm 6 #32 80 mm 80 mm Determine the following: 1. depth of the compression block 2. strain in the tension reinforcement 3. moment reduction factor 4. nominal moment capacity 5. ultimate moment capacity 6. actual steel ratio 7. minimum steel ratio 8. maximum steel ratio 9. Tension force 10. Compression force
Reinforced concrete solutions
REINFORCED CONCRETE
/ For the rectangular reinforced concrete beam (shown below),determine the stress at the upper and lower fibers of concrete and at steel reinforcement if fc'=20 MPa
Subject: Reinforced Concrete Design IS 456 A rectangular beam has a width of 300mm and an effective depth of 537.50 mm to the centroid of tension steel bars. Tension reinforcement consists of 6 - 28mm dia in two rows, compression reinforcement consists of 2 – 22mm dia, fc' = 27.6MPa, fy = 414.7MPa, d' = 60mm, L = 4m, the Unit weight of concrete is 24.56kN/cu.m If the beam is simply supported carrying a uniformly distributed dead load of 10kN/m, a uniformly distributed live load of 5kN/m, the safe concentrated live load that it could carry acting at the midspan is ______kN.
A rectangular beam has a width of 380 mm, effective depth of 445 mm, and overall depth of 510 mm and is reinforced with four No.29 tension bars. The concrete modulus of rupture fr = 3.65 MPa. The elastic modulus of the concrete and steel are, respectively, Ec =27,800 MPa and Es= 200,000 MPa. Determine if the beam will show hairline cracks due to a bending moment M = 108 kN-m and compute the relevant stresses. Provide material properties for concrete and reinforcing steel used in your design.
1. For the given singly reinforced beam section, fy =352 MPa, and f's = 28MPA. Calculate the required parameters for the different section condition in the table. d = 257mm h = 307mm 200mm Concrete Steel of Location Limit for No. of 16mm Area of diameter bar Condition Depth strain strain compression of block "a". neutral steel in to meet the axis "c". sq.mm. given beam condition. Units N/A N/A mm mm Sq.mm bars Balanced 0.003 Condition Compression 0.003 controlled Transition 0.003 controlled Tension 0.003 controlled