# Tutor profile: Maria C.

## Questions

### Subject: Basic Math

Solve $$3 \div 1/3 $$ = ?

Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. Therefore, $$3 \div 1/3 $$ can be rewritten as $$3 \times (3/1)$$ which is more easily solved and results in the answer $$3 \div 1/3 $$ = 9.

### Subject: Civil Engineering

A steel column is subjected to a service loads of DL = 150 kip and LL = 300 kip. The column is 25 ft long and is pinned at both ends in both the major and minor bending axis. Assuming A992 steel, determine an appropriate W14 shape using AISC. Use LRFD method for calculations.

First, the factored load $$P_u$$ must be determined from the provided service level loads. From ASCE 7, only load combination 1 applies since only dead and live loads are acting on the column. Therefore, the factored load is given by $$P_u$$ = $$1.2DL + 1.6LL = 1.2(150) + 1.6(300) = 705 kip $$ Next, determine the effective length $$KL$$.From AISC, the effective length factor for a pin-pin column is $$K = 1$$. Since the column is pin-pin in both about both $$r_x and r_y$$, the effective length is the same in both directions or $$KL_x = KL_y = KL$$ Therefore, $$KL$$ = $$1 \times L = 25 ft.$$ Third, determine the required design strength given by $$\phi P_n = \phi P_u$$. For compressive members, $$\phi = 1 $$. Therefore, $$\phi P_n = P_u = 705 kip.$$ Finally, an appropriate W14 shape can be selected from AISC. From AISC, a W14x90 has an available axial compressive strength of $$\phi P_n = 766kip$$ for $$KL = 24 ft$$ and $$\phi P_n = 709kip$$ for $$KL = 26 ft$$. Therefore, $$\phi P_n$$ for $$KL = 25ft$$ can be determined through interpolation to be $$\phi P_n = 709 + \frac{766 - 709}{24 - 26} (25 - 26) = 737.5 kip$$ Check $$\phi P_n > P_u$$ 737.5 kip > 705 kip therefore W14x90 OK

### Subject: Algebra

Write the equation of a line with a y-intercept of (0, 3) and a slope of $$\frac{-1}{2}.$$

The general equation of a line in slope intercept form is given by: $$y = mx + b$$ where m is the slope and b is the y-intercept. Therefore, the equation of a line with a y-intercept of (0, 3) and a slope of $$\frac{-1}{2}.$$ is $$y = \frac{-1}{2} x + 3.$$

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