ENG1001 Lecture 2: Week 2 Supports & Stability
30 May 2018
School
Department
Course
Professor
Struc&needs&to&have&at&least&enough&to&make&it&stable
But&extra&support&makes&calc& more&difficult
how&to&decide&if&struc&has¬&enough,&enough&or&excessive&support
Types
*while&drawings&for&pins&and&rollers&only&in&+ve&x-dir,&understood&that&they&
can&prov&reactn&in&-ve&dir&also
Supp…
Memb…
Reactions3that3occur
Fixed/b
uilt-in
Provides&3&reactions&
(for&2D):
Fx(force,&x-dir)&≠
0
•
FY&(force,&y-dir)&≠
0
•
MZ(applied&
moment,&z-dir)&≠
0
•
Can't&move&in&
any&dir&w/&
respect&to&
supp
(translate&or&
rotate)
Force&and&moment
Pin/hing
e
Provides&2&reactions&
(for&2D):
Fx(force,&x-dir)&≠
0
•
FY&(force,&y-dir)&≠
0
•
*Must&ensure&can't&be&
rotated&abt&pin&>>>&
maintain&rotational&eq
ΣM&abt&pin&
(applied&moment&
due&to&all&forces&
acting&on&struc&
abt&pin)&=&0
•
*Must&ensure&
Rotates
Can't&
translate
Force
Roller Provides&1&reaction&(for&
2D):
FY&(force,&y-dir)&≠
0
•
*Must&ensure&can't&be&
rotated&abt&roller&>>>&
maintain&rotational&eq
ΣM&abt&roller&
(applied&moment&
due&to&all&forces&
acting&on&struc&
abt&roller)&=&0
•
*Must&ensure&roller&
can't&be&translated&>>>&
maintain&translational&
eq
Fx&&@&roller&
(where&x&is&
direction&of&roller)&
=&0
•
Free&to&
rotate
Translates&in&
1&dir&only
Only&one&force&reaction
Free Provides&NO&reactions
Fx(force,&x-dir)&=&
0
•
FY&(force,&y-dir)&=&
0
•
MZ(applied&
moment,&z-dir)&=&
0
•
THREE3EQUIL.3EQNS!
Free&to&
rotate&and&
translate&w/&
respect&to&
supp
No&net&rctn.
In&equilibrium,&so&all&
forces&balanced&and&
structure&is&stable.
Eg
Telegraph&pole
Back&leg&of&chair&can&
swing&backwd,&but&
"fixed"&by&frictn
Roller&blades/
Skateboard&can&rotate&
freely,&and&can&
translate&in&dir&of&
wheels,&but&can't&
translate&into&ground&
or&perp.&to&rollers
Bearing&pads&on&
bridges
Flagpole
Joining3membs3tgt
Become&1&member
No3relative3transltn/rotn3betwn&2&joined&ends
In&diagram:
-full&penetration&butt&weld
-fully&bolted&connection
(eg.&by&single&bolt&connectn)
No&relative&transltn,&but&rotn3possible betwn&2&joined&ends
=&internal&pin/hinge&in&struc&(easier&construction)
Irrelevant&which&direction&you&initially&draw&pin&forces&initially
Internal&member&pin&forces&should&be&shown&to&be&equal&in&magnitude&and&
opposite&in&direction&on&opposite&sides&of&the&pin&
*if&sum&of&applied&moments&due&to&all&forces&acting&on&one&side&of&pin&≠ 0,&
struc&will&rotate&abt&pin&/&NOT&in&eq
ΣM&taken&to&one&side&of&pin&(applied&moment&due&to&all&forces&acting&
on&struc&abt&pin)&=&0
•
Exist&in&3-pin&arches
Determinate3or3indeterminate?
No.&of&rctns&supports&provide
=&3&>>>& determinate&(2&@&pin,&1&@&roller)
>3&>>>&indeterminate,&w/&alt&load&paths
**number&of&internal&pins&+&3&=&number&of&unknown&forces
<3&>>>&unstable,&struc¬&enough&support,&will&collapse
Stable
=&set&of&supports&provide&adequate&supp&to&prevent&struc&frm&
rotn/transltn
Has&load&path&frm&applied&load&to&supp
Unstable
=&set&of&supports&don't&prevent&rotn/transltn,&so&struc&will&collapse
No&load&path&frm&applied&load&to&supp
Determinate
=&has&just&enough&support&to&make&it&stable
>>&can&calc&exactly&how&much&of&applied&load&is&carried&by&each&support,&
using&eqns&of&eq&alone
Only&1&load&path&frm&an&applied&load&to&supp
Indeterminate
=&has&extra&support
>>&eqns&of&eq¬&enough&to&calc&how&much&of&applied&load&is&carried&by&
each&support
>1&load&path&frm&applied&load&to&support
>>&Proportion&of&load&carried&by&each&load&path&depends&on&stiffness&of&
various&load&paths
Week$2:$Supports$&$Stability
Saturday,&22&July&2017
16:19
Struc&needs&to&have&at&least&enough&to&make&it&stable
But&extra&support&makes&calc& more&difficult
how&to&decide&if&struc&has¬&enough,&enough&or&excessive&support
Types
*while&drawings&for&pins&and&rollers&only&in&+ve&x-dir,&understood&that&they&
can&prov&reactn&in&-ve&dir&also
Supp… Memb… Reactions3that3occur
Fixed/b
uilt-in
Provides&3&reactions&
(for&2D):
Fx(force,&x-dir)&≠
0
•
FY&(force,&y-dir)&≠
0
•
MZ(applied&
moment,&z-dir)&≠
0
•
Can't&move&in&
any&dir&w/&
respect&to&
supp
(translate&or&
rotate)
Force&and&moment
Pin/hing
e
Provides&2&reactions&
(for&2D):
Fx(force,&x-dir)&≠
0
•
FY&(force,&y-dir)&≠
0
•
*Must&ensure&can't&be&
rotated&abt&pin&>>>&
maintain&rotational&eq
ΣM&abt&pin&
(applied&moment&
due&to&all&forces&
acting&on&struc&
abt&pin)&=&0
•
*Must&ensure&
Rotates
Can't&
translate
Force
Roller
Provides&1&reaction&(for&
2D):
FY&(force,&y-dir)&≠
0
•
*Must&ensure&can't&be&
rotated&abt&roller&>>>&
maintain&rotational&eq
ΣM&abt&roller&
(applied&moment&
due&to&all&forces&
acting&on&struc&
abt&roller)&=&0
•
*Must&ensure&roller&
can't&be&translated&>>>&
maintain&translational&
eq
Fx&&@&roller&
(where&x&is&
direction&of&roller)&
=&0
•
Free&to&
rotate
Translates&in&
1&dir&only
Only&one&force&reaction
Free
Provides&NO&reactions
Fx(force,&x-dir)&=&
0
•
FY&(force,&y-dir)&=&
0
•
MZ(applied&
moment,&z-dir)&=&
0
•
THREE3EQUIL.3EQNS!
Free&to&
rotate&and&
translate&w/&
respect&to&
supp
No&net&rctn.
In&equilibrium,&so&all&
forces&balanced&and&
structure&is&stable.
Eg
Telegraph&pole
Back&leg&of&chair&can&
swing&backwd,&but&
"fixed"&by&frictn
Roller&blades/
Skateboard&can&rotate&
freely,&and&can&
translate&in&dir&of&
wheels,&but&can't&
translate&into&ground&
or&perp.&to&rollers
Bearing&pads&on&
bridges
Flagpole
Joining3membs3tgt
Become&1&member
No3relative3transltn/rotn3betwn&2&joined&ends
In&diagram:
-full&penetration&butt&weld
-fully&bolted&connection
(eg.&by&single&bolt&connectn)
No&relative&transltn,&but&rotn3possible betwn&2&joined&ends
=&internal&pin/hinge&in&struc&(easier&construction)
Irrelevant&which&direction&you&initially&draw&pin&forces&initially
Internal&member&pin&forces&should&be&shown&to&be&equal&in&magnitude&and&
opposite&in&direction&on&opposite&sides&of&the&pin&
*if&sum&of&applied&moments&due&to&all&forces&acting&on&one&side&of&pin&≠ 0,&
struc&will&rotate&abt&pin&/&NOT&in&eq
ΣM&taken&to&one&side&of&pin&(applied&moment&due&to&all&forces&acting&
on&struc&abt&pin)&=&0
•
Exist&in&3-pin&arches
Determinate3or3indeterminate?
No.&of&rctns&supports&provide
=&3&>>>& determinate&(2&@&pin,&1&@&roller)
>3&>>>&indeterminate,&w/&alt&load&paths
**number&of&internal&pins&+&3&=&number&of&unknown&forces
<3&>>>&unstable,&struc¬&enough&support,&will&collapse
Stable
=&set&of&supports&provide&adequate&supp&to&prevent&struc&frm&
rotn/transltn
Has&load&path&frm&applied&load&to&supp
Unstable
=&set&of&supports&don't&prevent&rotn/transltn,&so&struc&will&collapse
No&load&path&frm&applied&load&to&supp
Determinate
=&has&just&enough&support&to&make&it&stable
>>&can&calc&exactly&how&much&of&applied&load&is&carried&by&each&support,&
using&eqns&of&eq&alone
Only&1&load&path&frm&an&applied&load&to&supp
Indeterminate
=&has&extra&support
>>&eqns&of&eq¬&enough&to&calc&how&much&of&applied&load&is&carried&by&
each&support
>1&load&path&frm&applied&load&to&support
>>&Proportion&of&load&carried&by&each&load&path&depends&on&stiffness&of&
various&load&paths
Week$2:$Supports$&$Stability
Saturday,&22&July&2017 16:19
Document Summary
Struc needs to have at least enough to make it stable. But extra support makes calc more difficult how to decide if struc has not enough, enough or excessive support. *while drawings for pins and rollers only in +ve x-dir, understood that they can prov reactn in -ve dir also. Can"t move in any dir w/ respect to supp (translate or rotate) *must ensure can"t be rotated abt pin >>> maintain rotational eq. M abt pin (applied moment due to all forces acting on struc abt pin) = 0. *must ensure can"t be rotated abt roller >>> maintain rotational eq. M abt roller (applied moment due to all forces acting on struc abt roller) = 0. *must ensure roller can"t be translated >>> maintain translational eq. Fx @ roller (where x is direction of roller) Free to rotate and translate w/ respect to supp. In equilibrium, so all forces balanced and structure is stable. supp.
