W14x82 cols18 tall I882 in SolutionSolution a Time period T

W14x82 (cols.)-18\' tall I882 in

Solution

Solution:-

(a)

Time period (T) = 0.075 *(h)^0.75

                         = 0.075*(5.62)^0.75

                                       = 0.273 second

Response spectrum acceleration (S_a) = 1.49 g           ( from graph table)

                                                                         Answer

Design base shear (V_B) = A_h *W

                         A_h = Z/2 * I/R * S_a/g

                R = 3

                Z = 0.36

                 I = 1

A_h = 0.36/2 *1/3 *1.49 = 0.089

Base shear (V_B) = A_h * W

                           = 0.089 * 200

                        = 17.88 kips    Answer

(b) When load increase 40 kips

Then total load = 240 kips

Base shear (V_B) = 0.089 * 240 = 21.456 kips

Permissible base shear (V_B) = 1.49 * 17.88 = 26.64 kips

Here we see that permissible shear force is maximum than design shear force.

Structure is safe

Where S_a = 1.49 *g

(c) when load increase 60 kips

Then total load = 260 kips

Design base shear = 0.089 * 260

                                = 23.24 kips

Design base shear is less than permissible shear

So structure is safe.