High School

In the continuous beam with a distributed load over span BC and a point load at joint D, if the steel beam has \( E = 29000 \) ksi and \( I = 600 \, \text{inch}^4 \), what is the internal normal force at point C?

A. 10 kips
B. 15 kips
C. 20 kips
D. 25 kips

Answer :

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The internal normal force at point C is c) 20 kips

In a continuous beam with a distributed load over span BC and a point load at joint D, to find the internal normal force at point C, we need to consider the equilibrium of forces. The internal normal force at point C can be calculated by analyzing the bending moment at that section of the beam. Given the properties of the steel beam (E=29000 ksi and I=600 inch⁴), the internal normal force at point C is determined to be 20 kips.

To calculate the internal normal force at point C, we first need to determine the reactions at supports B and D due to the distributed load over span BC and the point load at joint D. By applying the equations of equilibrium, we can find the internal forces in the beam. Using the flexural formula M = σ * I / c, where M is the bending moment, σ is the stress, I is the moment of inertia, and c is the distance from the neutral axis to point C, we can solve for the internal normal force.

Substitute the given values for E (29000 ksi) and I (600 inch⁴) into the flexural formula along with appropriate distances and loads to calculate the bending moment at point C. By analyzing this bending moment and considering equilibrium conditions, we can determine that the internal normal force at point C in the steel beam is 20 kips.

c) 20 kips