# First moment of area

Attached i have put together 2 workings out side by side, They are both concerning shear flow at specific points of a box girder. My problem is calculating Q. Once calculation (second one) shows Q to be All the area above that point mulitplied by the distance from neutral axis, whereas the first working out shows Q to be only half the area above that point multiplied by the neutral axis. Can somebdy please clear up how to calculate Q

Thanks

#### Attachments

• Q.png
57.1 KB · Views: 777

## Answers and Replies

SteamKing
Staff Emeritus
Science Advisor
Homework Helper
Could you provide the complete problem from the textbook, rather than jumping straight into the calculations?

SteamKing
Staff Emeritus
Science Advisor
Homework Helper
You have to look at how the Qs are calculated in the problems.

In problem 7-50, Q was calculated for the section above the N.A. The problem asks for the shear flow in each side wall where the N.A. intersects the section. Each side has 1/2 of the total Q above the N.A. due to symmetry.

In problem 7-51, the problem asks for the shear flows at points C and D. The calculation of Q is different here because you are interested in the shear flow on only one side of the section, thus Q includes 1/2 of the top flange plus that portion of the side wall from the top flange down to point D.

Thank you for your thorough reply SteamKing, your explanation is very clear in what way to calculate Q however, im still unsure as to how to question asked for that, To me they see like the same question. If i got a question like this in an exam i would not know in which way i was supposed to calculate Q. Is it correct to say, the shear flow of a point along a line of symmetry is calculated by the total Q on either side of the line of symmetry? what would be the "rule" to calculate a point similar to D in 7-51?

SteamKing
Staff Emeritus
Science Advisor
Homework Helper
For a symmetric section like the rectangular box in Probs. 7-50 and 7-51, the shear flow will also be symmetric. In these cases, you pretend there is a cut at point C, where the top flange of the box section intersects the axis of symmetry. At point C, since the shear flow must be symmetric, it is reasonable to assume that q = 0. To find q at point D (as in Prob. 7-51), you calculate the first moment of area of the top and sides, w.r.t. the N.A., of all of the material between C and D. The total of these moments becomes Q.

In Prob. 7-50, the author chose to calculate the Q for all of the material above the N.A. and then divide by 2 to obtain Q at points A and A', and points B and B'. I think that his method of calculation in Prob. 7-50 should be modified, because it leaves the mistaken impression that there is a different method for calculating Q in this problem, than in Prob. 7-51.

• 1 person