Question

A one-story steel frame of 8 m span and 4 m height has the following properties: The second moments of cross-sectional area for beam and columns are Ib = 6500 cm4 and Ic = 1300 cm4, respectively; the elastic modulus for steel is 200,000 MPa. For purposes of dynamic analysis, the frame is considered massless with a mass of 50,000 kg lumped at the beam level; the columns are clamped at the base; the damping ratio is estimated at 5%.

(a) Determine the peak values of lateral displacement at the beam level and bending moments throughout the frame due to the design spectrum of Fig. 6.9.5 scaled to a peak ground acceleration of 0.5g.

Answer 1

The force exerted by each of the 10 braces to stabilize a 17.0 m high and 11.0 m long wall against wind pressure is calculated at 12,155 N, with the pressure applied at the center of the wall's area.

Step-by-step explanation:

Stability and Forces on Braced Wall

To calculate the force exerted by each brace on the wall due to wind pressure, we first need to find the total force acting on the wall. We multiply the pressure by the area of the wall:

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Total area of the wall = Height × Length = 17.0 m × 11.0 m = 187.0 m²

Total wind force = Area × Pressure = 187.0 m² × 650 N/m² = 121,550 N

This force acts at the center of area, which is halfway up the wall. Having 10 braces implies that the force is distributed equally among them:

Force per brace = Total wind force / Number of braces = 121,550 N / 10

Thus, the force per brace is 12,155 N parallel to the length of each brace.