WORKSHEET1 Loads, Supports, Moments and Equilibrium

A. loads Q1. a) what is the main force acting on and in buildings? gravity b) in what direction does it act? vertically downwards

A. loads Q2. a) what do loads do? tend to destabilise building - overturn tend to break elements deform elements - change of shape, deflection b) what must the structure do? produce reactions - provide equilibrium resist tendency to break - be strong enough

A. loads Q3. What are: a) Static loads? basically loads which when applied, do not move remain during the life of the building may be dead loads, live load (movable but static), settlements, thermal effects b) dynamic loads basically loads which move - change over time continuous - e.g. earthquakes, wind impact / instantaneous

A. loads Q3. What are: c) Dead loads? static - permanent loads - fixed (mostly vertical) weight of structure and elements, heavy built-ins & equipment d) Live loads static loads which may or may not be acting all the time occupants, contents, moveable partitions, snow e) What other loads are there? wind, earthquake, thermal, settlement, impact

A. loads Total Load = Dead Load + Live Load + Self-Weight Q4. What makes up the total load on a structure Total Load = Dead Load + Live Load + Self-Weight

A. loads kN kN / m kPa (kN / m2 ) Q5. What are the units for: a) a point or concentrated load? kN b) a load distributed over a length? kN / m c) a load distributed over an area? kPa (kN / m2 )

A. loads 1 kPa up -suction (roof pitch < 30o) Q6. a) In a non-cyclone area what is approximately the magnitude of the wind loads? 1 kPa b) If the roof on a house has a pitch of 27o, what is the direction of the wind load on the roof? up -suction (roof pitch < 30o) c) If the roof is of lightweight construction, weighing 0.3 kPa, what considerations need be taken into account? (i) securing the roof down - more nails, ties, etc (ii) making the roof heavier (may not be a design option)

B. supports M H V 3 - V, H & M 1 - V V 1 - V V 2 - V & H H V Q7. Draw and name the reactions that can be produced by: M a) a fixed support 3 - V, H & M H V b) a simple support 1 - V V c) a roller support 1 - V V d) a pinned support 2 - V & H H V

B. supports Q8. Draw the reactions that can be produced by the following structural systems. State whether the system is a mechanism, statically determinate or statically indeterminate (a) (b) (c) (d) (e) (f) a) statically determinate d) statically indeterminate b) statically indeterminate e) statically determinate c) statically indeterminate f) mechanism

C. moments 1kNm W * 4 = 1000 W = 250N A W1 200N W2 100N W 4m 2m Q9. Given the beam loaded as shown, calculate the weight, W required for equilibrium Taking moments about A clockwise moments = 200*2 + 100*6 1kNm = 400 + 600 = For equilibrium ∑M = 0 anticlockwise moments = 1kNm W * 4 = 1000 W = 250N

C. moments R L = 105 kNm RR * 6.5 = 105 RR = 16.15 kN RR + RL = 28 kN Q10. Given the simply supported beam loaded as shown: R L 1m 2m 1.5m 0.5m 4kN 8kN 10kN 6kN calculate the reactions, RL and RR For equilibrium ∑M = 0 taking moments about RL clockwise moments = 4*1 + 8*2.5 + 10*4.5 + 6*6 = 105 kNm = 4 + 20 + 45 + 36 anticlockwise moments = RR * 6.5 RR * 6.5 = 105 RR = 16.15 kN For equilibrium ∑M = 0 For equilibrium ∑V = 0 RR + RL = 28 kN RL = 28 - 16.15 RL = 11.85 kN

C. moments M 24 kN 96 kNm Q11. Given a cantilever beam 8m long loaded with a Uniformly Distributed Load (UDL) of 3 kN / m 8m 3 kN/m UDL M determine the moment reaction at the support total load on beam W = 24 kN 3 * 8 = can be taken to act at centre of beam 4m moment M = 24 * 4 = 96 kNm

C. moments = 92 kNm RR = 15.3 kN RL = 8.7 kN 2kN/m 1.5kN/m 2kN R 4m 6m Q12. Beam loadings in real structures are often complex. Consider a beam with a point load of 2kN on the end of an overhang with a UDL of 1.5 kN/m distributed over 2/3 of the main span. The beam also carries its own self-weight of 2kN/m. What are the values of the reactions, a) RL, b) RR 6kN 2kN R L 2m 4m 16kN Take moments about one of the reactions, e.g. RL (or RR ) Clockwise moments = (1.5*4)*2 + (2*8)*4 + 2*8 = 92 kNm Anticlockwise moments = RR*6 ∑M = 0 RR*6 = 92 RR = 15.3 kN ∑V = 0 RR+ RL = 6 + 16 + 2 = 24 RL = 8.7 kN

C. moments = 32 kNm Weight 20kN A Q13. The drawing on the right shows a lightweight prefabricated building. The total weight of the (empty) building is 20kN. The line of action of the wind load is 2m above the ground. Given a wind load of 16kN as shown: a) what is tending to overturn the building? the wind load of 16kN causes an overturning moment b) what is the overturning moment? in this case the overturning moment is the clockwise moment about A caused by the wind = 32 kNm overturning moment = 16 * 2

C. moments = 30 kNm yes since 32 > 30 Weight 20kN A Q13. The drawing on the right shows a lightweight prefabricated building. The total weight of the (empty) building is 20kN. The line of action of the wind load is 2m above the ground. Given a wind load of 16kN as shown: c) what is restraining the building? The weight of the building, 20kN, causes a restraining moment d) what is the restraining moment? the restraining moment is the anticlockwise moment as a result of the weight of the building = 30 kNm restraining moment = 20 * 1.5 yes since 32 > 30 e) will the building overturn?

C. moments 3m 2m 16kN Weight 20kN A Q13. The drawing on the right shows a lightweight prefabricated building. The total weight of the (empty) building is 20kN. The line of action of the wind load is 2m above the ground. Given a wind load of 16kN as shown: f) suggest two options that will make the building safer (i) increase the weight of the building to at least 32/1.5 = 21.4kN (ii) lower the height of the building so that the action of the wind is lowered by at least 125 mm (to 1.875m above ground) (iii) make the building base wider - at least 3.2 m wide (iv) tie the building down - fix it to the ground. It will act as a cantilever

D. equilibrium Q14. What are the three equations of equilibrium and what do they mean? a) SV = 0 the sum of all the vertical forces is equal to zero (at any point) the total downward forces equal the total upward forces the structure doesn’t move up or down b) SH = 0 the sum of all the horizontal forces is equal to zero (at any point) the total forces acting to the right equal the total forces acting to the left the structure doesn’t move to the left or right c) SM = 0 the sum of all the moments (about any point) the total clockwise moments equal the total anticlockwise moments the structure does not rotate/spin

D. equilibrium a) cross-bracing b) knee-bracing c) rigid joints Q15. Given the post-and beam arrangement as shown, describe three ways of stabilising it. Draw and name them. a) cross-bracing b) knee-bracing c) rigid joints d) solid infill (shear panels) e) build-in posts (rigid joints)