Question 1

The concrete beam above is reinforced with 3 steel cables with a diameter of 25 mm. Calculate the distance d required for the maximum stresses in the concrete and steel to meet the allowable stresses simultaneously. Also calculate the maximum M that can be applied.

>> This question is tricky and requires a slightly different approach to solve. The aim is to get our h' and d':

The concrete beam above is reinforced with 3 steel cables with a diameter of 25 mm. Calculate the distance d required for the maximum stresses in the concrete and steel to meet the allowable stresses simultaneously. Also calculate the maximum M that can be applied.

>> This question is tricky and requires a slightly different approach to solve. The aim is to get our h' and d':

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Question 1

Question 1

Step 1:
Transform steel into concrete and remove concrete taking tension

Step 1:
Transform steel into concrete and remove concrete taking tension

Step 2:
Use σ_allow limits to get 1st equation for h' and d

Step 2:
Use σ_allow limits to get 1st equation for h' and d

Step 3:
Use centroid condition for 2nd equation for h' and d

Step 3:
Use centroid condition for 2nd equation for h' and d

Step 4:
Use both equations to solve for h' and d

Step 4:
Use both equations to solve for h' and d

Step 5:
Calculate moment of inertia I

Step 5:
Calculate moment of inertia I

Step 6:
Use σ_allow to calculate M_max

Step 6:
Use σ_allow to calculate M_max

Useful formula:

Useful formula:

Question 1

Question 1

Step 1: Transform steel into concrete and remove concrete taking tension Step 1: Transform steel into concrete and remove concrete taking tension

Step 2: Use σallow limits to get 1st equation for h' and d Step 2: Use σallow limits to get 1st equation for h' and d

Step 3: Use centroid condition for 2nd equation for h' and d Step 3: Use centroid condition for 2nd equation for h' and d

Step 4: Use both equations to solve for h' and d Step 4: Use both equations to solve for h' and d

Step 5: Calculate moment of inertia I Step 5: Calculate moment of inertia I

Step 6: Use σallow to calculate Mmax Step 6: Use σallow to calculate Mmax

Useful formula: Useful formula:

Step 1:
Transform steel into concrete and remove concrete taking tension

Step 1:
Transform steel into concrete and remove concrete taking tension

Step 2:
Use σ_allow limits to get 1st equation for h' and d

Step 2:
Use σ_allow limits to get 1st equation for h' and d

Step 3:
Use centroid condition for 2nd equation for h' and d

Step 3:
Use centroid condition for 2nd equation for h' and d

Step 4:
Use both equations to solve for h' and d

Step 4:
Use both equations to solve for h' and d

Step 5:
Calculate moment of inertia I

Step 5:
Calculate moment of inertia I

Step 6:
Use σ_allow to calculate M_max

Step 6:
Use σ_allow to calculate M_max

Useful formula:

Useful formula: