Problem 1: A square concrete column with dimensions 22 x 22 in. is reinforced with a total of eight No. 10 bars arranged uniformly around the column perimeter. Material stress-strain are given by curves a and c in Fig 1. Calculate the percentages of total load carried by the concrete and the steel as load is gradually increased from 0 to failure, which is assumed to occur when the concrete strain reaches a limit value of 0.0030. Determine the load at strain increments of 0.0005 up to the failure strain, and graph your results, plotting load percentage vs. strain. (Source: Design of Concrete Structures 16th ed., McGraw-Hill, 2021) (Hint: use strain compatibility) fs. ksi 60 50 40 30 20 10 O T fc, ksi 9 5 4 3 2 I 0.001 a Steel b Concrete, fast loading c Concrete, slow loading d Elastic concrete 0.002 0.003

Problem 1: A square concrete column with dimensions 22 x 22 in. is reinforced with a total of eight No. 10 bars arranged uniformly around the column perimeter. Material stress-strain are given by curves a and c in Fig 1. Calculate the percentages of total load carried by the concrete and the steel as load is gradually increased from 0 to failure, which is assumed to occur when the concrete strain reaches a limit value of 0.0030. Determine the load at strain increments of 0.0005 up to the failure strain, and graph your results, plotting load percentage vs. strain. (Source: Design of Concrete Structures 16th ed., McGraw-Hill, 2021) (Hint: use strain compatibility) fs. ksi 60 50 40 30 20 10 O T fc, ksi 9 5 4 3 2 I 0.001 a Steel b Concrete, fast loading c Concrete, slow loading d Elastic concrete 0.002 0.003

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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Question

Problem 1:
A square concrete column with dimensions 22 x 22 in. is reinforced with a total of eight No.
10 bars arranged uniformly around the column perimeter. Material stress-strain are given
by curves a and c in Fig 1. Calculate the percentages of total load carried by the concrete
and the steel as load is gradually increased from 0 to failure, which is assumed to occur
when the concrete strain reaches a limit value of 0.0030. Determine the load at strain
increments of 0.0005 up to the failure strain, and graph your results, plotting load
percentage vs. strain. (Source: Design of Concrete Structures 16th ed., McGraw-Hill, 2021)
(Hint: use strain compatibility)
fs, ksi
60-
50
40
30
20
10
OL
fc, ksi
6
5
T
4
3
2
1
0
0.001
Es or Ec
Fig. 1
b
a Steel
b Concrete, fast loading
c Concrete, slow loading
d Elastic concrete
0.002
0.003

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Step 1: Introducing Given Data

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Step 2: Calculate area of steel & concrete

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Step 3: Sample calculation for strain of 0.0005

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Step 4: Calculation of percentage of load for steel & concrete for strain of 0.0005

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Step 5: Make the Load percentage table & plot the graph

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