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.

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