The cross section of a simply supported beam is given in the previous example. Length of the beam is L = 4 m. Determine the deflection at midspan. The beam is subjected to
a) a uniformly distributed load, p = 16 kN/m,
b) a concentrated load at the midspan, P = 32 kN.
(When M < Mcr use the uncracked cross section, while for M ≥ Mcr use the cracked cross section.)
Solve Problem
Problem a) Midspan deflection, v [mm]= Problem b) Midspan deflection, v [mm]=Solve
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Steps
Problem a) Step 1. Calculate the maximum (midspan) moment from the uniformly distributed load, p. Check whether the cross section is cracked. The cross section cracks. Cracking moment is determined in the previous problem (Problem 4.4). The cracked cross sectional properties must be used in the deflection analysis, which are also calculated in the previous problem. Step 2. Calculate the midspan deflection. Problem b) Step 1. Calculate the maximum (midspan) moment from the concentrated load, P. Check whether the cross section is cracked. The cross section cracks. Cracking moment is determined in the previous problem (Problem 4.4). The cracked cross sectional properties must be used in the deflection analysis, which are also calculated in the previous problem. Step 2. Calculate the midspan deflection.Step by step
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Check moment
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Results
Problem a) The maximum (midspan) moment from the uniformly distributed load, p is The cross section cracks. Cracking moment is determined in the previous problem (Problem 4.4). The cracked cross sectional properties must be used in the deflection analysis, which are also calculated in the previous problem. The midspan deflection is Problem b) The maximum (midspan) moment from the concentrated load, P is The cross section cracks. Cracking moment is determined in the previous problem (Problem 4.4). The cracked cross sectional properties must be used in the deflection analysis, which are also calculated in the previous problem. The midspan deflection isWorked out solution