Determine the maximum required tension strength and maximum

Determine the maximum required tension strength and maximum required compression strength of member CD using the following factored load combinations. W = 55 kips 12 ft. Eqn. 1 1.4D Eqn. 2 1.2D 1.6L Eqn. 3 1.2D1.0W+0.5L Eqn. 4 0.9D1.0w 9 ft. D = 7.5 kips L-15 kips W = 55 kips 12 ft. 12 ft. D-30 kips L-60 kips 3 kips (T) 0.25 kips kip 1 kip 1.6 kips (T 1 kip The wind can also blow from right to left such that member force CD is the same magnitude but is in compression

Solution

The given load diagrams can be used to determine the force in memeber CD

load in member CD due to a vertical load of 1 kip at A and 0.25 kip at C =3 kips(Tension)

Load in member CD due to 1 kip wind loads at A and C =1.6 kips

Dead load at A=30 kips and 7.5 kips at C. Therefore, load in member CD due to dead load=30*3=90 kips(tension)

Live load at A =60 kips and 15 kips at C.Therefore load in member CD due to live load=60*3=180 kips(tension)

Wind load acting in the direction show =55 kips at A and C

Force in CD due to wind load=55*1.6=88 kips(tension)

Load in CD due wind in opposite direction=88 kips(compression)

Let us determine the tension in member CD due to the load combinations:

1) 1.4D = 1.4*90=126 kips(tension)

2)1.2D+1.6L= (1.2*90)+(1.6*180) =396 kips(tension)

3)1.2D+1.0W+0.5L =(1.2*90)+(1*88)+(0.5*180) =286 kips(tension)

4)0.9D+1.0W =(0.9*90)+(1*88)=169 kips(tension

Max tension=396 kips

Determination of maximum compression

Maximum compression will be seen when wind blows in opposite direction

Load combination 4 will have maximum compression in member CD

Force in member CD due to 0.9D+1.0W =(0.9*90)-(1*88)=-7 kips=7 kips compression

Therefore the minimum required tension strength=396 kips

Maximum compression strength required = 7 kips