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Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 3.2 - Problem 12e
Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 3.2 - Problem 12e

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# In the article “Influence of Crack Width on Shear ISBN: 9780073401331 38

## Solution for problem 12E Chapter 3.2

Statistics for Engineers and Scientists | 4th Edition

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Problem 12E

Problem 12E

In the article “Influence of Crack Width on Shear Behaviour of SIFCON” (C. Fritz and H. Reinhardt, High Performance Fiber Reinforced Cement Composites: Proceedings of the International RILEM/ACI Workshop, 1992). the maximum shear stress τ of a cracked concrete member is given to be τ = τ0(l - k w), where τ0 is the maximum shear stress for a crack width of zero, wis the crack width in mm, and k is a constant estimated from experimental data. Assume k = 0.29 ± 0.05 mm-1. Given that τ0 = 50 MPa and w = 1.0 mm, both with negligible uncertainty, estimate τ and find the uncertainty in the estimate.

Step-by-Step Solution:

Solution :

Step 1 of 1:

The maximum shear stress of a cracked concrete member is .

Where the maximum shear stress for a crack width of zero is .

Here and w=1.0 mm.

A constant estimated from experimental data is k.

We assume that Our goal is :

a). We need to find the uncertainty in the estimate.

a).

Then the maximum shear stress of a cracked concrete member is .

Now we have to find the estimated of the maximum shear stress is We know that , and .    MPa

Therefore the estimated of the maximum shear stress is 35.5 MPa

Then we have to find the uncertainty in the estimate.

The uncertainty in the estimate bias correction is Where .

Here we are differentiating with respect to k.   Then,     Therefore the uncertainty in the estimate is 2.5

Step 2 of 1

##### ISBN: 9780073401331

Since the solution to 12E from 3.2 chapter was answered, more than 550 students have viewed the full step-by-step answer. This full solution covers the following key subjects: crack, width, shear, stress, uncertainty. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. The answer to “In the article “Influence of Crack Width on Shear Behaviour of SIFCON” (C. Fritz and H. Reinhardt, High Performance Fiber Reinforced Cement Composites: Proceedings of the International RILEM/ACI Workshop, 1992). the maximum shear stress ? of a cracked concrete member is given to be ? = ?0(l - k w), where ?0 is the maximum shear stress for a crack width of zero, wis the crack width in mm, and k is a constant estimated from experimental data. Assume k = 0.29 ± 0.05 mm-1. Given that ?0 = 50 MPa and w = 1.0 mm, both with negligible uncertainty, estimate ? and find the uncertainty in the estimate.” is broken down into a number of easy to follow steps, and 109 words. The full step-by-step solution to problem: 12E from chapter: 3.2 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM.

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